Question

Fill in the equation of the circle which has a diameter with endpoints (-3,2) and (1,-6).

Answer 1

The equation of the circle which has a diameter with endpoints (-3,2) and (1,-6) is x² + y² +6x - 4y -15 = 0.

What is circle?

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.

Learn more about circle.

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