write the standard form of the equation of the circle for which the endpoints of a diameter are (0,0) and (4,-6)

Given:

The endpoints of a diameter are (0,0) and (4,-6).

To find:

The equation of the circle.

Solution:

The endpoints of a diameter are (0,0) and (4,-6). So, the length of the diameter is

Now, radius is half of the diameter.

Center of the circle is the midpoint of the endpoints of a diameter.

Standard form of a circle is

where, (h,k) is center and r is radius.

The center of the circle is (2,-3) and radius is . So,

Therefore, the standard form of the circle is .

a

step-by-step explanation: