If the endpoints of the diameter of a circle are (−10, −8) and (−6, −2), what is the standard form equation of the circle?

 The standard form equation of the given circle is

Step-by-step explanation:  Given that the co-ordinates of the end-points of the diameter of a circle are (−10, −8) and (−6, −2).

We are to find the equation of the circle in standard form.

The mid-points of the diameter of a circle is the center of the circle.

So, the co-ordinates of the center of the circle are

Also, the length of the radius is equal to half of the length of the diameter of the circle.

So, the length of the radius is calculate using distance formula as follows:

Now, the standard equation of a circle with radius r units and center at (h, k) is given by

We have

center, (h, k) = (-8, -5)  and  radius, r = 5 units.

Therefore, the standard equation of the circle is

Thus, the standard form equation of the given circle is