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

Answer:

$\large\boxed{radius=\sqrt{97}}$

Step-by-step explanation:

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

The formula of a distance between two points:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

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

Substitute:

$r=\sqrt{(6-(-3))^2+(7-3)^2}=\sqrt{9^2+4^2}=\sqrt{81+16}=\sqrt{97}$

Answer 2

Answer:

Step-by-step 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)