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

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.

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Using $z$ from the plane equation on the hyperboloid equation what do you get? –  Sigur Dec 31 '12 at 16:45

## 1 Answer

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, $2x-3y=-7$.

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Nice +1. When I saw the question, I thought you may have contributed a visual, artistic graph like you do so well. How was the wedding ceremony? –  amWhy Feb 26 '13 at 3:04
@amWhy: Great! I have to go to the collage to teach and I am sleepy :-( –  Babak S. Feb 26 '13 at 3:06
Sleepiness can seem almost painful at times! –  amWhy Feb 26 '13 at 3:08