Question

Each point on the edge of a circle is equidistant from the center of the circle. The center of a circle is located at ( 6,3). Which point on th ey-axis could be on the circle if the distance from the center of the circle to the edge is 10 units?

Answer 1

(0, –5)

Explanation:

If you don't see this option there is another option, (0 , 11) is also correct

Answer 2

This describes a circle with center (h,k) = (6,3) and radius r = 10

That circle has the equation

(x-h)²+(y-k)² = r²

(x-6)²+(y-3)² = 10²

(x-6)²+(y-3)² = 100

Every point on the y-axis has 0 as its x-coordinate, so we
substitute x=0 in

(x-6)²+(y-3)² = 100

(0-6)²+(y-3)² = 100

(-6)²+(y-3)² = 100

36+(y-3)² = 100

(y-3)² = 64

y-3 = ±8

y = 3±8

y=3+8, y=3-8
y=11, y=-5

Two solutions: (0,11) and (0,-5)