If the endpoints of the diameter of a circle are (−8, −6) and (−4, −14), what is the standard form equation of the circle?

Equation of the circle is .

Solution:

The endpoints of the diameter of a circle are (–8, –6) and (–4, –14).

Center of the circle = Mid point of the diameter

Mid point formula:

Here,

Center of the circle = (–6, –10)

Radius is the distance between center and any endpoint of the diameter.

To calculate the radius using distance formula.

Here,

units

The standard form of the equation of a circle is

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

Here, center = (–6, –10) and

Equation of the circle is .

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