Mathematics: 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

HStep-by-step explanation:Y= (x+2)^2-52 to the left x+2=0 x=-25 dpwn...

Point q lies on the circle and has an x-coordinate

summer098890

15.01.2022

2 square root 5

Step-by-step 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

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

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

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

$y=\pm\sqrt{20}$

simplify

$y=\pm2\sqrt{5}$

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

The y-coordinate is positive

therefore

The y-coordinate of point Q is $2\sqrt{5}$

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