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February 23rd, 2012, 01:49 PM  #1  
Senior Member Joined: Jan 2010 Posts: 205 Thanks: 0  Finding equation of a circle Quote:
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 and x = 6/13 So I have 2 xvalues 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?  
February 23rd, 2012, 03:14 PM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: Finding equation of a circle
When you substitute 6 for x into either equation you should get 2 yvalues 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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