25) The endpoints of the diameter of a circle are (6, 5) and (−2, 3). Which equation represents the circle? A) (x − 2)2 + (y − 4)2 = 9 B) ( x+ 2)2 + (y + 4)2 = 16 C) (x − 2)2 − (y + 4)2 = 16 D) (x − 2)2 + (y − 4)2 = 17

Option D.

Step-by-step explanation:

It is given that the endpoints of the diameter of a circle are (6, 5) and (−2, 3). So, midpoint of these end point is the center of the circle.

So, center of the circle is (2,4).

Length of diameter of the circle is the distance between (6, 5) and (−2, 3).

So, radius of the circle is

Standard form of a circle is

where, (h,k) is center of the circle and r is radius.

Substitute h=2, k=4 and in the above equation.

Therefore, the correct option is D.

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step-by-step explanation:

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