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

Hence, equation of circle is:

Te end points of the diameter are given to be:

(−6, 6) and (6, −2).

We know that the center of the circle is the mid-point of the diameter.

and the coordinates of the mid-point (e,f) of (a,b) and (c,d) is calculated as:

Here we have (a,b)=(-6,6) and (c,d)=(6,-2).

Hence, the coordinates of center (e,f) is calculated as:

Hence, center is located at: (0,2)

Now, the radius of circle is the the distance between the center and a point on the circle.

i.e. distance between (0,2) and (6,-2).

We know that the distance between two points (a,b) and (c,d) is calculated as:

Here we have (a,b)=(0,2) and (c,d)=(6,-2)

Hence, the length of the radius is calculated as:

Hence, the equation of the circle with center (h,k) and radius r is given by:

Hence, the equation of circle is:

Hence, equation of circle is:

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step-by-step explanation: