Gaukhar M.

asked • 11/28/20# ellipse, please help

Find the standard form for the equation of a circle(x−h)^2+(y−k)^2=r^2with a diameter that has endpoints (−6,8) and (9,3).

## 1 Expert Answer

(h, k) is the center of the circle

If our endpoints are (-6,8) and (9,3), then the center is halfway between the two:

- (-6 + 9) / 2 = 1.5
- (8 + 3) / 2 = 5.5

Therefore, (h,k) = (1.5, 5.5)

r is the radius.

The length of the diameter can be found using the distance formula and the diameter's endpoints:

- √((-6-9)
^{2}+ (8-3)^{2}) = √(225 + 25) = 15.8

r = diameter/2 = 7.9

Equation:

(x-h)^{2} + (y-k)^{2} = r^{2}

(x-1.5)^{2} + (y-5.5)^{2} = (7.9)^{2}

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Gaukhar M.

k=, h=, r= ?11/28/20