Answer:
(D) [tex](x-0)^2+(y-2)^2=52[/tex]
Step-by-step explanation:
It is given that the endpoints of the diameter of a circle are (−6, 6) and (6, −2).
Now, the standard form equation of the circle is:
[tex](x-a)^2+(y-b)^2=r^2[/tex]
where (a,b) are the coordinates of the center and r is the radius.
In order to find the center, first find the midpoint of the two given points, that is:
[tex]C=(\frac{-6+6}{2}, \frac{6-2}{2})[/tex]
[tex]c=(0,2)[/tex]
Thus, the center is (0,2).
Now, the radius is the distance from the center to either of the two given points, therefore using distance formula,
[tex]r^2=(-6-0)^2+(6-2)^2[/tex]
[tex]r^2=52[/tex]
Also, the equation of the circle is:
[tex](x-0)^2+(y-2)^2=52[/tex]
Hence, option D is correct.
