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

Find the equation of a circle whose center on the line 8x + 5y = 8 and passes through the points (2, 1) and (3, 5).

__Solution__:

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

The center of a circle is located along the line 8x + 5y = 8 and passes through the points (3, 5) and (2, 1). (Photo by Math Principles in Everyday Life) |

To get the radius of a circle, we need to use the distance of two points formula as follows

Next, we need another equation which is 8x + 5y = 8 in order to solve for x and y which is the coordinates of the center of a circle. Multiply equation (1) by 4, we have

Subtract the above equation from the equation of a line, we have

Substitute the value of y to the equation of a line in order to get the value of x, we have

Hence, the center of a circle is C (-3/2, 4). The radius of a circle is

Therefore, the equation of a circle is