Find the equation of a circle that has a diameter with the endpoints given by the points A(-4,9) and B (- 2, - 3) )

The equation of the circle is

Explanation:

Given that the endpoints of the circle are A(-4,9) and B(-2,-3)

We need to determine the equation of the circle.

Center:

The center of the circle can be determined using the midpoint formula,

Substituting the coordinates A(-4,9) and B(-2,-3), we get,

Thus, the center of the circle is (-3,3)

Radius:

The radius of the circle can be determined using the distance formula,

Substituting the center (-3,3) and the endpoint (-4,9), we get,

Thus, the radius of the circle is

Equation of the circle:

The standard form of the equation of the circle is given by

where (a,b) is the center and r is the radius.

Substituting the values, we have,

Thus, the equation of the circle is