Question

If the xy- plane The graph of the equation (x-6)^2+ (y+5^2)= 16 is a circle. point p is on the circle and has coordinates (10, -5). If PQ is a diameter of the circle, what are the coordinates of Q?

Answer 1

(x - 6)² + (y + 5)² = 16 is a circle centered at (6, -5) with a radius of 4 units.

The point P(10, -5) has the same y-coordinate as the center of the circle and it is placed 4 units to the right of it.

Then, the point Q must have the same y-coordinate and must be placed 4 units to the left of the center, therefore its x-coordinate is 6 - 4 = 2. In consequence, point Q is placed at (2, -5), as can be seen in the next graph: