In the xy -plane, the graph of the equation above is a circle. Point P is on the circle and has coordinates (10, -5). If  is a diameter of the circle, what are the coordinates of point Q?

The correct answer is: (2, -5)

Step 1 of 3 :
In the xy-plane, the given equation of a circle is 
So, the coordinate of the center is (6, -5) and the radius is 4 unit.
Step 2 of 3:
 is the diameter of the circle.
Point P is on the circle and has coordinates (10,- 5). Observe that the y-coordinates of point P and the center of the circle are the same, viz. - 5. So, since Q is at the other end of
diameter , hence the y-coordinate of Q should be - 5.
Step 3 of 3:
Let, the coordinates of point Q be (x, y).
Then, 
From the given points in the options, only the points 2, - 5) and (6, - 5) have the y-coordinate of - 5.
Intuitively, we can observe that the  portion in (×) becomes zero and we are left with  part. If we put x = 2, then it gives us , which becomes 8 as we take square-root of it.
Thus, the point (2, -5) satisfies (×).
Final Answer:
The coordinates of point Q is-A) (2, -5).