Question

Point Q lies on the circle and has an x-coordinate of 4.

Which value could be the y-coordinate for point Q?
2 square root 5
4 square root 2
2 Square root 13
8 Square root 2

Answer 1

A

Explanation:

Answer 2

2 square root 5

Explanation:

see the attached figure to better understand the problem

we know that

The equation of the circle is equal to

`(x-h)^2+(y-k)^2=r^2`

where

(h,k) is the center and r is the radius of the circle

In this problem we have

center at (0,0) and radius equal 6 units

so

`x^2+y^2=6^2\\x^2+y^2=36`

Remember that

If a point lie on the circle, then the point must satisfy the equation of the circle

Substitute the x-coordinate of point Q in the equation of the circle and solve for the y-coordinate of point Q

For x=4

`4^2+y^2=36\\y^2=36-16\\y^2=20`

`y=\pm√(20)`

simplify

`y=\pm2√(5)`

The point Q lie on the first Quadrant (see the picture)

The y-coordinate is positive

therefore

The y-coordinate of point Q is
`2√(5)`