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 the y-axis could be on the edge of the circle of the distance from the center of the circle to the edge is 10

Answer 1

(0, –5)

Explanation:

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

Answer 2

Good evening

Answer:

(0 , 5) and (0 , 11)

Explanation:

Suppose M(x , y) is a point of the circle of center (6,3) and radius 10 and M is also a point of the y-axis then the coordonates of M should verify these two equations at the same time:

`\left \{ {(x-6)^(2) +(y-3)^2=10^(2) } \atop {x=0}} \right.`

Then

(0-6)² + (y-3)² = 100

then

36 + (y-3)² = 100

then

(y-3)² = 100 - 36

= 64

then

|y-3| = 8

then

y - 3 = 8 or y - 3 = -8

then

y = 11 or y = 5

then the only points that are on the edge of the circle and on y-axis are:

(0 , 5) and (0 , 11).

:)