__Category__: Analytic Geometry, Plane Geometry, Algebra"Published in Vacaville, California, USA"

Find the equation of a circle that passes through the points of intersection of the circles x

^{2}+ y

^{2}= 5 and x

^{2}+ y

^{2}- x + y = 4, and through the point (2, -3).

__Solution__:

To illustrate the problem, it is better to draw the figure as follows

A circle that passes through the intersection of two circles and a point. (Photo by Math Principles in Everyday Life) |

Since the given two circles are non-concentric with their points of intersection, then the equation of another circle can be written as

where k is a constant that represents a family of non-concentric circles. To solve for the value of k, substitute the values of x and y from the given point, we have

Therefore, the equation of a circle is