Question

Susan knows that the coordinates of the center of a circle and a point on the circle are (-3, 2) and (10, -2), but she can't remember which coordinate pair is which. What could be an equation of the circle? Explain your answer.

Answer 1

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Answer:

(x +3)² +(y -2)² = 185

(x -10)² +(y +2)² = 185

Explanation:

One possible equation comes from using one of the points as center. The other possible equation comes from using the other point as center.

The radius can be found from the distance formula:

r² = (x2-x1)² +(y2-y1)² = (10-(-3))² +(2-(-2))² = 169 +16 = 185

The circle formula is ...

(x -h)² +(y -k)² = r² . . . . . . for center (h, k) and radius r

The above equations and the ones shown in the attachment are possibilities.