Question

The point (-3, 2) lines on a circle whose equation is (x + 3)2 + ( + 1)2 = r2. Which of

the following must be the radius of the circle?

Answer 1

3 units

Explanation:

Equation of the circle is:

`(x+3)^2 +(y+1)^2=r^2`

`\therefore [x-(-3)] ^2 +[(y-(-1)] ^2=r^2`

Equating it with

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

We find: h = - 3 & k = - 1

Center of the circle (C) = (-3, - 1)

Since, the point (-3, 2) lies on the circle, therefore radius of the circle wii be equal to the distance between the center of the circle (-3, - 1) and the point (-3, 2) which is on the circle.

Therefore,

`r = √([-3-(-3)]^2 +[2-(-1)]^2)`

`r = √([-3+3]^2 +[2+1]^2)`

`r = √([0]^2 +[3]^2)`

`r = √(0 +9)`

`r = √(9)`

`r = 3\: units`