Question

Circle O has a center at (-2, -2) and a diameter of 10 units. What point lies on circle O?

(-6, -5)

(-2, -2)

(6, 4)

(8, 8)

Answer 1

The point r(-6,-5) lies on the circle.

Step-by-step explanation

Given that the center of the circle=(-2,-2)

diameter=10 units

we have to determine which point among the given points lies on the circle.

radius=diameter/2=10/2=5 units

let (x,y) be a point on the circle

The distance between the center and (x,y) is equal to the radius of the circle

The distance between them=
`√((x-(-2))^2+y-(-2))^2)=5\\\\ √((x+2)^2+(y+2)^2) =5\\\\`

squaring both sides
`(x+2)^2+(y+2)^2=25\\`

The option (-6,-5) satisfies the equation

therefore the point that lies on the circle is (-6,-5)