Question

Determine the equation of the circle graphed below.

Answer 1

(x - 2)² + (y + 4)² = 29

Explanation:

Standard form

(x - h)² + (y - k)² = r²

(h, k) is the center and ris the radius

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For center (2, -4)

(x - 2)² + (y + 4)² = r²

use the distance formula to find d² which is the same as r²

r² = d² = (x2 - x1)² + (y2 - y1)²

r² = (4 - 2)² + (1 - -4)²

r² = 2² + 5²

r² = 29

Now the equation becomes

(x - 2)² + (y + 4)² = 29