The point (3,-6) is an endpoint to a diameter of circle P. The equation x^2+y^2-6x+2y=15 represents circle P. What is the y-coordinate of the other endpoint on this diameter?

Question

The point (3,-6) is an endpoint to a diameter of circle P. The equation x²+y²-6x+2y=155 represents circle P. What is the y-coordinate of the other endpoint on this diameter?

Answer 1

Answer 2

First, will need to do completing the square to find the center of the circle.

x²-6x +y²+2y = 15 Using the (-6/2)² = 9 for the x term, add 9 to both sides

x²-6x+9+y²+2y = 15+9 Using the (2/2)² = 1 for the y term, add 1 to both sides

x²-6x+9+y²+2y+1 = 15+9+1 Factor and simplify

(x-3)²+(y+1)² = 25

The center is at (3,-1)

5 units directly below that is the point given, (3,-6)

If you go 5 points above the center, that will be the other end of the diameter,

(3,4) The y coordinate is 4