What is the equation of the circle when given the endpoints of a diameter (-2, 15) and (6, -13)?

or

Step-by-step explanation:

Method 1:

For finding the radius:

The distance between points and is:

Substitute = (-2, 15) and = (6, -13):

Which is the diameter

The radius:

The centre:

The midpoint of two endpoints:

Center is (2,1)

The standard form:

Circle with radius r and centre (a,b) is

Expanding to get the general form:

Method 2:

Let the locus be the circle:

By angle in a semi-circle, The angle inscribed in a semicircle is always a right angle (90°).

This means line joining from one endpoint of diameter is perpendicular to the line joining from another endpoint, two lines always have the product of slope = -1: