Question

Point P(1,7) is located on circle C. The center of circle Cis (-2, 3). What is the radius of the circle?

A
5
B
3
С
D6

Answer 1

5 units

Explanation:

Hi there!

Equation of a circle:
`(x-h)^2+(y-k)^2=r^2` where the circle is centered at
`(h,k)` and r is the radius

1) Plug in the center (-2,3)

`(x-(-2))^2+(y-3)^2=r^2\\(x+2)^2+(y-3)^2=r^2`

2) Plug in the given point P(1,7) and solve for r

`(1+2)^2+(7-3)^2=r^2\\(3)^2+(4)^2=r^2\\9+16=r^2\\25=r^2`

Take the square root of both sides

`√(25) =√(r^2) \\5=r`

Therefore, the radius of the circle is 5 units.

I hope this helps!