Ronan

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12 years, 77 days
East Grinstead, United Kingdom

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These are answers submitted by Ronan

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The set of equations; as far as I can see, cannot be solved explicitly do to the trig. functions.
I rearranged your equations so you only need to solve eq5 and eq6 for y and z.

I randomly made up values for  t, T, a,c,e,f just to show the use of fsolve. 

Hope this helps you.

Edit I re-attached the worksheet because I had a mistake in it.


 

restart

t:=Pi/2;
T:=t;

(1/2)*Pi

 

(1/2)*Pi

(1)

a:=3;c:=2;e:=4;f:=2

3

 

2

 

4

 

2

(2)

#z:=1

 w := sqrt(a^2 - (a - y)^2);
v := cot(t + arcsin(w/a)) ;
 u := (sqrt(c^2 - (c - z)^2) - v*x - w)/x^2;
 x := y + z + e;
eq5 := v + cot(T + arcsin((u*x^2 + v*x + w)/c)) + 2*u*x = 0;
eq6 :=f = Pi/30*(6*u^2*x^5 + 15*u*v*x^4 + (20*u*w + 10*v^2)*x^3 + 30*v*w*x^2 + 30*x*w^2) - Pi/3*(-z^3 + 3*z^2*c - y^3 + 3*y^2*a);

(9-(3-y)^2)^(1/2)

 

-(9-(3-y)^2)^(1/2)/((3-y)^2)^(1/2)

 

((4-(2-z)^2)^(1/2)+(9-(3-y)^2)^(1/2)*x/((3-y)^2)^(1/2)-(9-(3-y)^2)^(1/2))/x^2

 

y+z+4

 

-(9-(3-y)^2)^(1/2)/((3-y)^2)^(1/2)-(4-(2-z)^2)^(1/2)/((2-z)^2)^(1/2)+2*((4-(2-z)^2)^(1/2)+(9-(3-y)^2)^(1/2)*(y+z+4)/((3-y)^2)^(1/2)-(9-(3-y)^2)^(1/2))/(y+z+4) = 0

 

2 = (1/30)*Pi*(6*((4-(2-z)^2)^(1/2)+(9-(3-y)^2)^(1/2)*(y+z+4)/((3-y)^2)^(1/2)-(9-(3-y)^2)^(1/2))^2*(y+z+4)-15*((4-(2-z)^2)^(1/2)+(9-(3-y)^2)^(1/2)*(y+z+4)/((3-y)^2)^(1/2)-(9-(3-y)^2)^(1/2))*(y+z+4)^2*(9-(3-y)^2)^(1/2)/((3-y)^2)^(1/2)+(20*((4-(2-z)^2)^(1/2)+(9-(3-y)^2)^(1/2)*(y+z+4)/((3-y)^2)^(1/2)-(9-(3-y)^2)^(1/2))*(9-(3-y)^2)^(1/2)/(y+z+4)^2+10*(9-(3-y)^2)/(3-y)^2)*(y+z+4)^3-30*(9-(3-y)^2)*(y+z+4)^2/((3-y)^2)^(1/2)+30*(y+z+4)*(9-(3-y)^2))-(1/3)*Pi*(-y^3-z^3+9*y^2+6*z^2)

(3)

 fsolve({ eq5,eq6},complex);

{y = -0.5302494488e-1+0.8720213598e-1*I, z = .1023238140-.3150972913*I}

(4)

 


 

Download 2024-05-13_A_An_approach.mw

f:=x-> (1-k*x)/(1+x^2)
f := proc (x) options operator, arrow; (1-k*x)/(1+x^2) end proc

slpf:=diff(f(x),x)
                           k      2 (-k x + 1) x
                slp := - ------ - --------------
                          2                 2   
                         x  + 1     / 2    \    
                                    \x  + 1/    

m:=eval(slpf,x=3);# slope of tangent line at x=3

                              2      3 
                         m := -- k - --
                              25     50

f(3)
                            3      1 
                          - -- k + --
                            10     10

line:=unapply(m*x+c,x)
 line := proc (x) options operator, arrow; ((2/25)*k-3/50)*x+c 

    end proc




line(3)=f(3);# x=3 is tangent point
                  6      9          3      1 
                  -- k - -- + c = - -- k + --
                  25     50         10     10

c:=solve(line(3)=f(3),c)
                               27     7 
                        c := - -- k + --
                               50     25

line(x)
                   /2      3 \     27     7 
                   |-- k - --| x - -- k + --
                   \25     50/     50     25

 

Check under Tools Options Display Typesetting level to see if it is set to extended.  

@dharr  I appear to have the setup working in principal. I created seperate worksheets. One for the Main Package and one for the Sub Package. Both attached.  I have hilighted the differences in both in red. Then I copied both help files across to the correct location. They now list correctly in Help. 

 

New_RT_Edit_Dadabase_2024.mw

New_UHG_Edit_Dadabase_2024.mw

Interesting problem.  I found this method in the RealDomain help page.

restart;

n:=3;m:=2;
eqx:=x^(n/m)=a;
use RealDomain in (maple_sol:=solve(eqx,[x]))[] end use;  #also tried solve()
F:=map(X->eval(eqx,X),maple_sol);
map(X->evalb(X),F);
                             n := 3

                             m := 2

                               (3/2)    
                       eqx := x      = a

                          [     (2/3)]
                          [x = a     ]

                          F := [a = a]

                             [true]

This is rather similar to the 1st question I asked on MaplePrimes. I just happened to look at it today

Dual sum loop with a condition - MaplePrimes  

restart

 

for n from 1 to 10 do
add(add(add(`if`(i+j+k<=n, 1/(i*j*k),0),i=1..n),j=1..n),k=1..n);
end do;

0

 

0

 

1

 

5/2

 

17/4

 

49/8

 

967/120

 

801/80

 

4523/378

 

84095/6048

(1)

 

 

Download A_2024-03-15_Sum_with_Condition.mw

This is a way using seq

M := Matrix(4, 4, [[m[1, 1], m[1, 2], m[1, 3], m[1, 4]], 
                   [m[2, 1], m[2, 2], m[2, 3], m[2, 4]],
                   [m[3, 1], m[3, 2], m[3, 3], m[3, 4]],
                   [m[4, 1], m[4, 2], m[4, 3], m[4, 4]]]);

L:=[seq(M[1 .. 4, i], i = 1 .. 4)];

whattype(L[3]);

 

I am sure there are more direct ways.1st, I changed you numbers just to see if this works more generally. Works with you numbers too

a:=evalf(1119.8*21/101)
                        a := 232.8297030

b:=trunc(a)
                            b := 232

c:=evalf(a-b)
                         c := 0.8297030

d:=evalf(c,2)
                           d := 0.83

b+d
                             232.83

with your numbers
a:=evalf(3*21/100,3);
                           a := 0.630

b:=trunc(a)
                             b := 0

c:=evalf(a-b)
                           c := 0.630

d:=evalf(c,2)
                           d := 0.63

b+d
                              0.63

Your code has so many errors. Are you typing it in a text editor? Hard to see how you could enter that much code in maple and not notice or find errors along the way.

This runs but I cannot verify you logic.

I used the VS code editor to find the errors. and maplemint That might help you.

Cong:=proc(n)
 local  a,b,An,Bn,Cn,Dn:
if n mod 2 = 1  then  
  An:=0:   
  Bn:=0:    
  for a from (round(-sqrt(n/(2)))) to round(sqrt(n/(2)) ) do           
     for b  from (round(-sqrt(n)) )to round(sqrt(n) )do                
          if is( (sqrt(n-2*a^(2)-b^(2)) )/(32),integer  ) then 
               An:=An+1 ;               
             elif is((sqrt(n-2*a^(2)-b^(2)) )/(8) ,integer )  then                   
               Bn:=Bn+1 ;
          end if:          
     end do: 
  end do:
 end if; 
if 2*An=Bn  then
    print(True); 
  else 
   print(False);
end if; 
if n mod 2 = 0 then
    Cn:=0: 
    Dn:=0:
end if;          
for a  from (round(-sqrt(n/(8)))) to round(sqrt(n/(8)) ) do          
    for b  from (round(-sqrt(n/(2)))) to round(sqrt(n/(2))) do                
        if is((sqrt(n/(2)-4*a^(2)-b^(2)) )/(32), integer   ) then                  
              Cn:=Cn+1 ;               
          elif is((sqrt(n/(2)-4*a^(2)-b^(2)) )/(8) ,integer) then
            Dn:=Dn+1 ;
        end if:
    end do: 
end do:  
if 2*Cn=Dn then
    print("True");  
  else  
    print("False");
end if;  
end proc;

maplemint(Cong);
Cong(108);

 

If I am intrepetering things correctly.  Your

diff((z - zA)*(z - zB)*(z - zC), z)*I);   # I removed semicolin inside brackets

gives a 2nd order polynomial (quadratic)   .say it is Q(Z)    Why have you multiplied the whole diff eqn. by I 

solve(Q(z) , z ,explicit)   #gives two roots which are supposed to be the focii of the ellipse.

Look on Marden's theorem - Wikipedia

This is a really useful procedure I found here on Primes  years ago. Called factrix. though in this case it pulls out (-1/2) instead of (1/2)
Edit:- the link to the reference to factrix  How do I extract common factors in a matrix? - MaplePrimes

[moderator: Copyrighted code removed. Source is factrix by Robert Israel, part of his Maple Advisor Database.]

You have to expand the equation. 

if  expand((x+1)^2=x^2+2*x+1) then print(1) else print(0) fi

or

if  expand((x+1)^2)=x^2+2*x+1 then print(1) else print(0) fi

 

I parameterised the points on the ellipse. I made them projective points [x,y,1] in the form of vectors. Reason the equation of the  line through two projective points is the Cross Product of the two points as another vector . P1 X P2  = L12 Now the intersect point of two lines as vectors is L1 X L2= Pintersect.

A line in vector form <a , b, c>   represents a*x + b*y + c=0

The use of factrix by @Robert B. Isreal  reduces the projective vectors, as in projective geometry vectors can be scaled without changing the answers.

Edit:- Correction.  Replece this into the document.  The intersection points were scaled incorrectly.

The 3 collinear points

for i to 3 do
    pPint || i := convert(Pint || i[1 .. 2]/Pint || i[3], list);
    eval(pPint || i, pramsplot);
    evalf(%);
end do;


 

restart

NULLNULL

NULL

with(LinearAlgebra)

LinePts := proc (p1, p2) description " Calculates a line through two points"; (p2[2]-p1[2])*x+(p1[1]-p2[1])*y-p1[1]*p2[2]+p1[2]*p2[1] end proc

proc (p1, p2) description " Calculates a line through two points"; (p2[2]-p1[2])*x+(p1[1]-p2[1])*y-p1[1]*p2[2]+p1[2]*p2[1] end proc

(1)

factrix := proc (M) local Mt, t, v, f, i, j, m, n, q, S, Si, res, u; options `Maple Advisor Database 1.01 for Maple 6`, `Copyright (c) 2000 by Robert B. Israel.  All rights reserved`; Mt := M; if not type(Mt, {Matrix, Vector}) then Mt := evalm(Mt) end if; if hastype(eval(Mt), float) then S := map(proc (t) options operator, arrow; t = `tools/gensym`(f) end proc, indets([flatten(Mt)], float)); Mt := map2(subs, S, Mt); Si := map(proc (e) options operator, arrow; rhs(e) = lhs(e) end proc, S) else Si := {} end if; if type(Mt, matrix) then m := linalg[rowdim](Mt); n := linalg[coldim](Mt); v := factor(q*add(add(f[i, j]*Mt[i, j], i = 1 .. m), j = 1 .. n)); t, u := selectremove(hastype, v, f[anything, anything]); Mt := subs(q = 1, [seq([seq(coeff(t, f[i, j]), j = 1 .. n)], i = 1 .. m)]); if hastype(M, matrix) then Mt := matrix(Mt) end if elif type(Mt, vector) then m := linalg[vectdim](Mt); v := factor(q*add(f[i]*Mt[i], i = 1 .. m)); t, u := selectremove(hastype, v, f[anything]); Mt := subs(q = 1, [seq(coeff(t, f[i]), i = 1 .. m)]); if hastype(M, vector) then Mt := vector(Mt) end if elif type(Mt, Matrix) then m := LinearAlgebra:-RowDimension(Mt); n := LinearAlgebra:-ColumnDimension(Mt); v := factor(q*add(add(f[i, j]*Mt[i, j], i = 1 .. m), j = 1 .. n)); t, u := selectremove(hastype, v, f[anything, anything]); Mt := Matrix(m, n, proc (i, j) options operator, arrow; subs(q = 1, coeff(t, f[i, j])) end proc) elif type(Mt, Vector) then m := LinearAlgebra:-Dimension(Mt); n := VectorOptions(Mt, orientation); v := factor(q*add(f[i]*Mt[i], i = 1 .. m)); t, u := selectremove(hastype, v, f[anything]); Mt := Vector(m, proc (i) options operator, arrow; subs(q = 1, coeff(t, f[i])) end proc, orientation = n) else ERROR(M, `does not evaluate to a matrix, vector, Matrix or Vector`) end if; if type(Mt, {Matrix, Vector}) then subs(res = u, q = 1, Si, delayDotProduct(res, Mt)) else subs(res = u, q = 1, Si, res*(eval(Mt))) end if end proc

proc (M) local Mt, t, v, f, i, j, m, n, q, S, Si, res, u; options `Maple Advisor Database 1.01 for Maple 6`, `Copyright (c) 2000 by Robert B. Israel.  All rights reserved`; Mt := M; if not type(Mt, {Matrix, Vector}) then Mt := evalm(Mt) end if; if hastype(eval(Mt), float) then S := map(proc (t) options operator, arrow; t = `tools/gensym`(f) end proc, indets([flatten(Mt)], float)); Mt := map2(subs, S, Mt); Si := map(proc (e) options operator, arrow; rhs(e) = lhs(e) end proc, S) else Si := {} end if; if type(Mt, matrix) then m := linalg[rowdim](Mt); n := linalg[coldim](Mt); v := factor(q*add(add(f[i, j]*Mt[i, j], i = 1 .. m), j = 1 .. n)); t, u := selectremove(hastype, v, f[anything, anything]); Mt := subs(q = 1, [seq([seq(coeff(t, f[i, j]), j = 1 .. n)], i = 1 .. m)]); if hastype(M, matrix) then Mt := matrix(Mt) end if elif type(Mt, vector) then m := linalg[vectdim](Mt); v := factor(q*add(f[i]*Mt[i], i = 1 .. m)); t, u := selectremove(hastype, v, f[anything]); Mt := subs(q = 1, [seq(coeff(t, f[i]), i = 1 .. m)]); if hastype(M, vector) then Mt := vector(Mt) end if elif type(Mt, Matrix) then m := LinearAlgebra:-RowDimension(Mt); n := LinearAlgebra:-ColumnDimension(Mt); v := factor(q*add(add(f[i, j]*Mt[i, j], i = 1 .. m), j = 1 .. n)); t, u := selectremove(hastype, v, f[anything, anything]); Mt := Matrix(m, n, proc (i, j) options operator, arrow; subs(q = 1, coeff(t, f[i, j])) end proc) elif type(Mt, Vector) then m := LinearAlgebra:-Dimension(Mt); n := VectorOptions(Mt, orientation); v := factor(q*add(f[i]*Mt[i], i = 1 .. m)); t, u := selectremove(hastype, v, f[anything]); Mt := Vector(m, proc (i) options operator, arrow; subs(q = 1, coeff(t, f[i])) end proc, orientation = n) else ERROR(M, `does not evaluate to a matrix, vector, Matrix or Vector`) end if; if type(Mt, {Matrix, Vector}) then subs(res = u, q = 1, Si, delayDotProduct(res, Mt)) else subs(res = u, q = 1, Si, res*(eval(Mt))) end if end proc

(2)

NULL

NULL

NULL

Firstly Paramaterise a conic centred on the Origin using projective points

Conic := proc (x, y) options operator, arrow; a*x^2+b*y^2+c*x*y+d end proc

proc (x, y) options operator, arrow; a*x^2+b*y^2+c*x*y+d end proc

(3)

sol1 := solve(eval(Conic(x, y), y = 0), x)

(-a*d)^(1/2)/a, -(-a*d)^(1/2)/a

(4)

NULL

xint := `assuming`([combine(simplify(sol1[2]))], [a::real, a > 0, d < 0])

-(-d/a)^(1/2)

(5)

linet := LinePts([xint, 0], [0, t])

t*x-(-d/a)^(1/2)*y+(-d/a)^(1/2)*t

(6)

sol2 := solve([Conic(x, y), linet], [x, y]); map(allvalues, %)

[[x = -(-d/a)^(1/2), y = 0], [x = -(-d/a)^(1/2)*(b*t^2+d)/(c*(-d/a)^(1/2)*t+b*t^2-d), y = t*(c*(-d/a)^(1/2)*t-2*d)/(c*(-d/a)^(1/2)*t+b*t^2-d)]]

(7)

CparmPt := `<,>`(rhs(sol2[2, 1]), rhs(sol2[2, 2]), 1)

Vector[column](%id = 36893490806110780580)

(8)

CparmPt := unapply(CparmPt, t)

proc (t) options operator, arrow; rtable(1 .. 3, {1 = -(-d/a)^(1/2)*(b*t^2+d)/(c*(-d/a)^(1/2)*t+b*t^2-d), 2 = t*(c*(-d/a)^(1/2)*t-2*d)/(c*(-d/a)^(1/2)*t+b*t^2-d), 3 = 1}, datatype = anything, subtype = Vector[column], storage = rectangular, order = Fortran_order) end proc

(9)

NULLCparmPt(t)

Vector[column](%id = 36893490806134464372)

(10)

Create 6 Projective Ponits on the conic

P0 := CparmPt(t[0])

Vector[column](%id = 36893490806134620156)

(11)

P1 := CparmPt(t[1])

Vector[column](%id = 36893490806134630388)

(12)

P2 := CparmPt(t[2])

Vector[column](%id = 36893490806134722556)

(13)

P3 := CparmPt(t[3])

Vector[column](%id = 36893490806134740980)

(14)

P4 := CparmPt(t[4])

Vector[column](%id = 36893490806134845436)

(15)

P5 := CparmPt(t[5])

Vector[column](%id = 36893490806127228916)

(16)

Create 6 Projective Lines through pairs of Ponits P0P4, P0P5:  P1P3, P1P5:  P2P3, P2P4 uning crossproduct of vectors

 

l04 := op(2, factrix(`&x`(P0, P4)))

Vector[column](%id = 36893490806134060444)

(17)

 

l05 := op(2, factrix(`&x`(P0, P5)))

Vector[column](%id = 36893490806134290060)

(18)

l13 := op(2, factrix(`&x`(P1, P3)))

Vector[column](%id = 36893490806188406652)

(19)

l15 := op(2, factrix(`&x`(P1, P5)))

Vector[column](%id = 36893490806188440500)

(20)

l23 := op(2, factrix(`&x`(P2, P3)))

Vector[column](%id = 36893490806188465316)

(21)

l24 := op(2, factrix(`&x`(P2, P4)))

Vector[column](%id = 36893490806130202612)

(22)

Get 3 intersection points in projective form

Pint1 := op(2, factrix(`&x`(l04, l13)))

Vector[column](%id = 36893490806134736044)

(23)

Pint2 := op(2, factrix(`&x`(l05, l23)))

Vector[column](%id = 36893490806192605772)

(24)

Pint3 := op(2, factrix(`&x`(l15, l24)))

Vector[column](%id = 36893490806145831988)

(25)

From a square matrix using the 3 points. If the determinant is 0 the points are colinear

M := `<|>`(Pint1, Pint2, Pint3)

Matrix(%id = 36893490806102267172)

(26)

Determinant(M)

0

(27)

Plotting

play with t_0 ..t_5 to move the points on the Conic

pramsplot := [a = 2, b = 1, c = -1, d = -4, t[0] = 1/10, t[1] = 1/2, t[2] = -1/3, t[3] = -9/10, t[4] = 55, t[5] = -8]

[a = 2, b = 1, c = -1, d = -4, t[0] = 1/10, t[1] = 1/2, t[2] = -1/3, t[3] = -9/10, t[4] = 55, t[5] = -8]

(28)

 

NULL

for i from 0 to 5 do p || i := convert(P || i[1 .. 2], list) end do

[-(-d/a)^(1/2)*(b*t[5]^2+d)/(c*(-d/a)^(1/2)*t[5]+b*t[5]^2-d), t[5]*(c*(-d/a)^(1/2)*t[5]-2*d)/(c*(-d/a)^(1/2)*t[5]+b*t[5]^2-d)]

(29)

ll := proc (v::Vector) options operator, arrow; x*v[1]+y*v[2]+v[3] end proc

proc (v::Vector) options operator, arrow; x*v[1]+y*v[2]+v[3] end proc

(30)

ll04 := ll(l04)

x*((-d/a)^(1/2)*t[0]*a*c+(-d/a)^(1/2)*t[4]*a*c-2*t[0]*t[4]*a*b+t[0]*t[4]*c^2-2*a*d)+y*(2*(-d/a)^(1/2)*t[0]*a*b+2*(-d/a)^(1/2)*t[4]*a*b+t[0]*t[4]*b*c-d*c)-2*(-d/a)^(1/2)*t[0]*t[4]*a*b+2*(-d/a)^(1/2)*a*d+t[0]*c*d+t[4]*c*d

(31)

ll05 := ll(l05)

x*((-d/a)^(1/2)*t[0]*a*c+(-d/a)^(1/2)*t[5]*a*c-2*t[0]*t[5]*a*b+t[0]*t[5]*c^2-2*a*d)+y*(2*(-d/a)^(1/2)*t[0]*a*b+2*(-d/a)^(1/2)*t[5]*a*b+t[0]*t[5]*b*c-d*c)-2*(-d/a)^(1/2)*t[0]*t[5]*a*b+2*(-d/a)^(1/2)*a*d+t[0]*c*d+t[5]*c*d

(32)

ll13 := ll(l13)

x*((-d/a)^(1/2)*t[1]*a*c+(-d/a)^(1/2)*t[3]*a*c-2*t[1]*t[3]*a*b+t[1]*t[3]*c^2-2*a*d)+y*(2*(-d/a)^(1/2)*t[1]*a*b+2*(-d/a)^(1/2)*t[3]*a*b+t[1]*t[3]*b*c-d*c)-2*(-d/a)^(1/2)*t[1]*t[3]*a*b+2*(-d/a)^(1/2)*a*d+t[1]*c*d+t[3]*c*d

(33)

ll15 := ll(l15)

x*((-d/a)^(1/2)*t[1]*a*c+(-d/a)^(1/2)*t[5]*a*c-2*t[1]*t[5]*a*b+t[1]*t[5]*c^2-2*a*d)+y*(2*(-d/a)^(1/2)*t[1]*a*b+2*(-d/a)^(1/2)*t[5]*a*b+t[1]*t[5]*b*c-d*c)-2*(-d/a)^(1/2)*t[1]*t[5]*a*b+2*(-d/a)^(1/2)*a*d+t[1]*c*d+t[5]*c*d

(34)

ll23 := ll(l23)

x*((-d/a)^(1/2)*t[2]*a*c+(-d/a)^(1/2)*t[3]*a*c-2*t[2]*t[3]*a*b+t[2]*t[3]*c^2-2*a*d)+y*(2*(-d/a)^(1/2)*t[2]*a*b+2*(-d/a)^(1/2)*t[3]*a*b+t[2]*t[3]*b*c-d*c)-2*(-d/a)^(1/2)*t[2]*t[3]*a*b+2*(-d/a)^(1/2)*a*d+t[2]*c*d+t[3]*c*d

(35)

ll24 := ll(l24)

x*((-d/a)^(1/2)*t[2]*a*c+(-d/a)^(1/2)*t[4]*a*c-2*t[2]*t[4]*a*b+t[2]*t[4]*c^2-2*a*d)+y*(2*(-d/a)^(1/2)*t[2]*a*b+2*(-d/a)^(1/2)*t[4]*a*b+t[2]*t[4]*b*c-d*c)-2*(-d/a)^(1/2)*t[2]*t[4]*a*b+2*(-d/a)^(1/2)*a*d+t[2]*c*d+t[4]*c*d

(36)

The 3 collinear points

NULL

for i to 3 do pPint || i := convert(Pint || i[1 .. 2], list); eval(pPint || i, pramsplot); evalf(%) end do

[-430., -1748.992977]

(37)

``

plots:-display(plots:-implicitplot([eval(Conic(x, y), pramsplot), eval(ll04, pramsplot), eval(ll05, pramsplot), eval(ll13, pramsplot), eval(ll15, pramsplot), (eval(ll23, pramsplot)).(eval(ll24, pramsplot))], x = -3 .. 3, y = -5 .. 5, colour = [red, green, pink, blue, yellow, grey, orange]))

 

NULL

NULL

NULL


 

Download 2023-12-23_A_Pascal_Conic_parameterised.mw

You basically have a 5th order polynomail in h. In general there is no explicit solution for a 5th order or higher polynomial.

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