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February 23rd, 2012, 01:49 PM   #1
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Finding equation of a circle

A circle with the equation: x^2 + y^2 -8x = 0
and a hyperbola with the equation: (x^2 / 9) - (y^2 / 4) = 1
intersect at points A and B.
If a new circle is created with a diameter of AB, what is the equation of the new circle?
So first I solved for y^2 in the given circle's equation to substitute into the equation of the given hyperbola:

Subtract "x^2" from both sides and add 8x to both sides:
y^2 = 8x -x^2

Replace y^2 into the given hyperbola's equation:
(x^2 / 9) - ((8x - x^2) / 4) = 1

Simplify the second part in the equation:
(x^2 / 9) - 2x + (x^2 / 4) = 1

Multiply both sides by 36:
4x^2 - 72x + 9x^2 = 36

Combine like terms and set equal to 0:
13x^2 - 72x - 36 = 0

Use the quadratic formula and I got the solutions:
x = 6
x = -6/13

So I have 2 x-values which I assume both are intersections made by the circle and parabola, but without graphing anything, how do I find AB?

Okay, I just tested out -6/13 for both the original circle and parabolic equations, and it comes out to an imaginary number so I guess there's no such points on them.

So one of the points is (6, sqrt(12)). How do I find the other point of intersection?
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February 23rd, 2012, 03:14 PM   #2
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Re: Finding equation of a circle

When you substitute 6 for x into either equation you should get 2 y-values when you take the square root. If then .

So, you would have a circle with center (6,0) and radius or:

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