Items tagged with circle

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I have to find the tangent lines to the circle x^2+y^2+6*x-8*y+25 = 1/16 which pass at the O(0;0) 

So i make a general line y=m * x

Ho can i put m*x instead of y in the circle and calculate the delta of the equation that i get?


I want to calculate the intersection between three circles.
I know that in this case i can calculate intersection of only the first and second equation, but I need this for a interactive component.

The command "intersection"[GEOMETRY] work only with 2 circles.

I did this but it doesn't work.


Parametric equation of a circle in 3d by three points. Draghilev method.


In some cases when dealing with vectofields an such the are integral has to be expressed in terms of r(t).

the general form for r is r^2=(r*cos(t)-a)^2+(r*sin(t)-b)^2, When I solve this in maple it seems like I get the inverse of the desired result.

If I knew that was always the case I could just inverse my result to get the right expression for r, but im not sure if it only applies for this particular cas or all cases.

I would be happy if anyone took a quick look and suggested a way to obtain the desired solution for any center (a,b) for the circle.



Expression for radius, circle centred at (a,b)

RA := r^2 = (r*cos(t)-a)^2+(r*sin(t)-b)^2

r^2 = (r*cos(t)-a)^2+(r*sin(t)-b)^2


isolate(r^2 = (r*cos(t)-a)^2+(r*sin(t)-b)^2, r)

r = (1/2)*(a^2+b^2)/(cos(t)*a+b*sin(t))


eval(%, [a = -1, b = 0])

r = -(1/2)/cos(t)


plot3d([-2*x, x^2+y^2], y = -sqrt(-x^2-2*x) .. sqrt(-x^2-2*x), x = -2 .. 0, color = [green, red], orientation = [0, 0, 0])


(1/2)*Pi <= t and t <= 3*Pi*(1/2)

(1/2)*Pi <= t and t <= (3/2)*Pi


0 <= r and r <= -2*cos(t)

0 <= r and r <= -2*cos(t)


Area_off_center = int(r, [r = 0 .. -2*cos(t), t = (1/2)*Pi .. 3*Pi*(1/2)]); 1; Area_at_center = int(r, [r = 0 .. 1, t = 0 .. 2*Pi])

Area_off_center = Pi


Area_at_center = Pi






I would also happily like to know how I can solve for the range r can take, obviously in the example i´m working with here r starts at 0, but that is not always the case i guess.


Thank you, your help is much apperciated

how to Prove that the circumference of a circle of radius r is 2πr
on maple ?????

  Hi, there

How can I draw the excircles, incircles,circumcircle and their centers of a triangle simultaneously with maple13 in a geometric plot? please specify the commands.

many thanks for your help


Suppose I have the parametric equations of a circle



where t runs from 0 to 2*pi. How can I show the orientation of this parametric curve on a plot?

Dear all,

I want to plot for example cos(theta) from 0 to 2*Pi inside a circle at a radius R. The axis theta of the ploted function is at a radius R.

Is it possible ?


i want to plot a circle which is centered at(0,0),and the radius is the length of Point2 and origin

but it shows some error,how could i do to solve this

i want to plot a circle with that centered at (0,0),and the radius is the length of Point2 and orgin

but it shows the error

how could i do to solve this









I want to find a point has coordinates are integer numbers and write the equation of tangent line to a given circle,  knowing that, the points of tangent has also integer coordinates. For example, the circle has centre M(-1,-5) and radius R=5. I tried





eqS:=Equation(circle(S,(a-HorizontalCoord(M))^2 + (b-VerticalCoord(M))^2 -R^2=0,[a,b],'centername'=T)):


for a from -50 to 50  do

for b from -50 to 50  do

if  a <>HorizontalCoord(M) and b<>VerticalCoord(M) and eqS then

L:=[op(L), [a,b]] fi;

od: od:


eqS:=Equation(circle(S,(x-HorizontalCoord(M))^2 + (y-VerticalCoord(M))^2 -R^2=0,[x,y],'centername'=T));

k:=[seq](sort(Equation(TangentLine(P, S, point(A, pt[])), [x,y])), pt in L):



> with(combinat):


for i from 1 to nops(d) do  


end do;

If I want to the point of intersection of two lines which are not perpendicular line, for example

[[-3*x-4*y-48 = 0, 4*x+3*y-6 = 0], [[x = 24, y = -30]]]

How can I select?



c1 := circle([0, 0], 1, color = red);
p2 := implicitplot(x = 1/2, x = -2 .. 2, y = -1 .. 1.1, colour = blue, linestyle = 1, thickness = 2);
display(c1, p2);

How to fill that part beetween line and circle(where x>1/2 in circle )?

Hello everyone!

I have a question that I can't seem to find a straight answer to. I need to fit a circle to a collection of points that a circular in nature. I was trying to use the following elliptical least squares fit, but I can't determine what I should be minimizing.

Here's the page:


For an ellipse, I used the general conic:


I minimize using:



What would I use for a circle? Or is there a better way for a circle?

"Circular segment" is the unfortunate but standard term for the region between a chord and an arc of a circle sharing the same endpoints (see  I say "unfortunate" because the phrase suggests a line segment when it actually means a planar region.

I would like to plot a shaded circular segment using Maple17.  I want the endpoints of the chord & arc to be anything I please, so the chord is not necessarily horizontal, or vertical, or the diameter of the circle, etc.

At the URL

there is an image containing a shaded circular segment, but I don't see what code produced the image.  The image there includes a horizontal chord, and I don't know if the code used to produce that image can be adapted for chords that are not horizontal.

If I have to, I can plot a shaded polygon with a huge number of sides that is indistinguishable from a circular segment.  I have plotted polygons before.  But it would obviously be preferable to plot a shaded circular segment.

If there a way to plot two curves of the form r = f(theta) and shade the region between them?  This would be better than the huge-polygon approach, but not as good as a simple command for plotting a shaded circular segment, if such a command exists.

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