You want find the intersection of the two curves
x^2 - (y-6)^2 = 36, which is a hyperbola, with
y = -x^2 , which is a downwards parabola
use substitution.
form y = -x^2, x^2 = -y
into the first:
-y - (y^2 - 12y + 36) = 36
-y - y^2 + 12y - 36 - 36 = 0
y^2 -11y + 72 = 0
There are no real solutions to this equation, so
there is no solution to the system of equations,
check:
https://www.wolframalpha.com/input/?i=plot+x%5E2-(y-6)%5E2%3D36,+y%3D-x%5E2
x^(2)-(y-6)^(2)=36 and y=-x^(2)
Solve the equation
1 answer