My Math Forum Finding equation of a circle

 Algebra Pre-Algebra and Basic Algebra Math Forum

February 23rd, 2012, 01:49 PM   #1
Senior Member

Joined: Jan 2010

Posts: 205
Thanks: 0

Finding equation of a circle

Quote:
 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
and
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?

 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 y-values when you take the square root. If $y^2=12$ then $y=\pm2\sqrt{3}$. So, you would have a circle with center (6,0) and radius $2\sqrt{3}$ or: $(x-6)^2+y^2=12$

 Tags circle, equation, finding

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post nickqqqq1 Algebra 4 April 12th, 2013 02:56 PM soulrain Algebra 7 January 5th, 2012 07:51 PM berkeleybross Algebra 4 December 8th, 2010 07:15 PM dewjr Algebra 2 November 25th, 2010 12:00 PM aschenbr.rach Calculus 1 March 7th, 2010 11:52 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top