The equation of the circle which has a diameter with endpoints (-3,2) and (1,-6) is x² + y² +6x - 4y -15 = 0.
Circle is the 2D geometry which is round in shape with radius R.
The diameter with endpoints (-3,2) and (1,-6). is
D = √ [(1+3)²+(-6-2)²]
D = 8.944 units
Radius of circle is R = D/2
R = 8.944 units /2
R =4.4721 units
Given is the general form of the equation of a circle passing through a point and having radius R is
(x -h)² +(y - k)² = R²
Substitute the coordinate (h,k) = (-3,2) and radius R = 4.4721
(x +3)² +(y - 2)² = 4.471²
x² + y² +6x - 4y +5 = 20
x² + y² +6x - 4y -15 = 0
Thus, the equation of the circle which has a diameter with endpoints (-3,2) and (1,-6) is x² + y² +6x - 4y -15 = 0.
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