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Find the equation of a circle that passes through the points of intersection of the circles x2 + y2 = 5 and x2 + y2 - x + y = 4, and through the point (2, -3).
Solution:
To illustrate the problem, it is better to draw the figure as follows
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| 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
