Question

Find the exact solutions of x^2-(y-6)^2=36 and y=-x^2 ?? I'm getting an imaginary answer, is that correct?

Answer 1

well you are looking for the points of intersection between the curves

rewrite the 2nd equation as x^2 = -y and substitute into the 1st equation

-y - (y -6)^2 = 36

-y -(y^2 - 12y + 36) = 36

so

-y^2 + 11y - 72 = 0

divide by -1 gives

y^2 -11y + 72 = 0

so yes you get complex solutions, and I think thats why they have asked for the exact solutions

hope this helps

Answer 2

Yes it does! Thanks, I was just looking for a second opinion, I appreciate it!