MHB Help find eqn of circle given another circle that is tangent

[sktrinh]

Please help me find the standard equation of the circle passing through the point (−3,1) and containing the points of intersection of the circles

x^2 + y^2 + 5x = 1

and

x^2 + y^2 + y = 7

I don't know how to begin, I am used to tangent lines or other points, but I don't know what is visually going on here. I can find the two centres C(h,k) of the given equations (-5/2,0) & (0,-1/2) both with r = sqrt(29/4), but what is the conceptual trick to equate that to the equation in question? Thanks for your help.

 

[MarkFL]

Re: help find eqn of circle given another circle that is tangent

I would begin by finding the points of intersection of the two given circles. We know these points will lie on the line perpendicular to the line containing the centers and that is midway between the centers.

 

[johng1]

Re: help find eqn of circle given another circle that is tangent

Hi,
I agree with Mark for your specific circles. In general for two given circles and a point P not on the line of intersection of the circles, you want to find the equation of the circle passing through the intersection points and P. To do this first find the intersection points Q and R of the two circles. Then find the circumcircle of points P, Q and R. Here's an excellent web page that, among other things, gives algorithms for these two problems:
Circle, Cylinder, Sphere