Find the exact solutions of x^2 - (y - 12)^2 = 144 and y = -x^2.

Question

No solution?

Answer 1

second verse, same as the first:
y = -x^2, so

x^2 - (-x^2 - 12)^2 = 144
x^2 - x^4 - 24x^2 - 144 = 144
x^4 + 23x^2 + 288 = 0
again, the discriminant is negative, so there are no solutions.

x=0 works only in the 2nd equation
(±12,12) only works in the first equation

Answer 2

Thank you!