Question

Find the exact solutions of x^2 - (y - 6)^2 = 36 and y = -x^2.

(0,0), (6,6), and (-6,6)?

Answer 1

Hmmm.
y = -x^2 so

x^2 - (-x^2-6)^2 = 36
x^2 - x^4 - 12x^2 - 36 = 36
x^4 + 11x^2 + 72 = 0
I don't see any real solutions. 11^2-4*72 < 0

Answer 2

Thanks

Answer 3

And yet, I do see that your points work.
Hmmm.

Answer 4

No, they don't they fit the first equation, but not the 2nd.

Only (0,0) works in both

Answer 5

Nope. (0,0) does not work in the 1st.
0 - 36 ≠ 36

Can't believe I let you fool me! :-)

Answer 6

At this point, I'm fooling myself!:-)

Answer 7

(0-6)^2=36
(-6)^2=36
36=36