If (−4, 11) and (−6, 5) are the endpoints of a diameter of a circle, what is the equation of the circle?

The equation of the circle is = (x +5)² + (y -8)² = 10.

Step-by-step explanation:

Step 1; The given coordinates are taken as (x1, y1) and (x2, y2). So

(x1, y1) = (-4, 11) and (x2, y2) = (-6, 5).

The midpoint of the circle, (h, k) = (, ).

For the given circle, (h, k) = (, ) = (-5, 8)

Step 2; To find the distances between the midpoint (-5, 8)  and another point on the circle (-6, 5), we use the formula

Distance = √ (x2 - x1)² + (y2 - y1)².

Distance between (-4, 11) and (-6, 5) is,

Distance = √ (-6 - (-4))² + (5 - 11)² = √ 4 + 36 = √40 = Radius of the cirlce (r).

Step 3; The equation of a circle is given by (x -h)² + (y -k)² = r².

So the equation is (x +5)² (y -8)² = (√10)² = 10.

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