MaplePrimes - answers and comments on Question, Equation of a circle

Error

Kitonum — Sun, 05 Feb 2012 16:09:19 Z

There is a serious mistake in your decision! Why do you define the line l in such a strange way, taking on it arbitrarily point C? This line is already defined by its equation! And if you specify another point C, you would get a different line.

I would write your code like this:

restart: with(geometry):

point(A,-1,5):

point(B,-2,-2):

point(T,a,b):

line(l,3*x-4*y-27=0,[x,y]):

sys:=solve([distance(T,A) = distance(T,B), distance(T,A)=distance(T,l)],[a,b]):

point(o, rhs(sys[1,1]), rhs(sys[1,2])):

point(K, rhs(sys[2,1]), rhs(sys[2,2])):

sort(Equation(circle(c1,[o,distance(o,A)],[x,y]))); # First solution

sort(Equation(circle(c2,[K,distance(K,A)],[x,y]))); # Second solution

Thank you

toandhsp — Sun, 05 Feb 2012 18:07:16 Z

First, many thanks to Kitonum. Because i want to have a beautiful answer, therefore, i write the equation circle passing three points A, B, C. And then, write the equation tangent of the circle (ABC) at the point C. Thus, the line is this equation of this tangent. Now, i hope Kitonum understand my idea. Thank you again.

Answers are correct

Markiyan Hirnyk — Sun, 05 Feb 2012 18:08:04 Z

Both answers by the questioner are correct:

and