If the endpoints of the diameter of a circle are (−8, −6) and (−4, −14), what is the standard form equation of the circle? a) (x + 6)2 + (y + 10)2 = 20 b) (x − 6)2 + (y − 10)2 = 20 c) (x + 6)2 + (y + 10)2 = 2 5 d) (x − 6)2 + (y − 10)2 = 2 5

Step-by-step explanation:

The standard form of an equation of a circle:

(h, k) - center

r - radius

We have the endpoints of the diameter of a circle (-8, -6) and (-4, -14).

The midpoint of a diameter is a center of a circle.

The formula of a midpoint:

Substitute:

We have h = -6 and k = -10.

The radius is the distance between a center and the point on a circumference of a circle.

The formula of a distance between two points:

Substitute (-6, -10) and (-8, -6):

Finally we have