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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
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| 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
