SOLUTION: A circle has a center of (-5,3) and passes through point (-1,7). Write an equation that represents the circle.

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Question 705922: A circle has a center of (-5,3) and passes through point (-1,7). Write an equation that represents the circle.
Found 2 solutions by solver91311, josgarithmetic:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


A circle centered at with radius is represented by the equation: .

You are given the values for and , and the value of is the distance from your given center to the given point on the circle. Use the distance formula:



So



where and are the coordinates of the given points.

John

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Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Use distance formula to calculate the radius, the length from the point on the circle, (-1,7), and the center, (-5,3).
Using r for radius, r=sqrt%28%28-1-%28-5%29%29%5E2%2B%287-3%29%5E2%29
=sqrt%28%284%29%5E2%2B%284%29%5E2%29=sqrt%2832%29

Your circle's equation is %28x%2B5%29%5E2%2B%28y-3%29%5E2=r%5E2, and you can find r^2 from the previous use of the calculation of r.