Question

Find the radius of a circle, given that the center is at (3,-3) and the point (7,6) lies on the circle.

Answer 1

Explanation:

if center is (3,-3), then we know the equation must look like:

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

Now to make sure (7,6) lies on the circle, we plug in:

(7-3)^2+(6+3)^2=16+81=97

so r= sqrt(97)

Answer 2

`\large\boxed{radius=√(97)}`

Explanation:

The radius is the distance between the center and any point on the circle.

The formula of a distance between two points:

`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

We have the center (3, -3) and other point on the circle (7, 6).

Substitute:

`r=√((6-(-3))^2+(7-3)^2)=√(9^2+4^2)=√(81+16)=√(97)`