How to show that two planes meet a hyperboloid in circles which lie on a sphere

Question

How to show that the planes $2x+3z=5$ and $2x-3y+7=0$ meet the hyperboloid

$-x^2+3y^2+12z^2$=$75$ in circles which lie on the sphere

$3$$x^2+3y^2+3z^2+4x+36z-110=0$ please help.

Answer 1

Hint: Find $x$ from $2x+3z=5$ and put it into hyperbolid equation. Next do the same for shpere. you will find the same equation. It means the circle you found by doing first step is the equation which satisfies the equation of the sphere. Do the same action with another plane, $2x-3y=-7$.