Is the point (−2, 10) on the circle with radius 5 and center (2, 13)?

The point can be demonstrated to lie on the circle by plotting both on a graph. It can also be shown to lie on the circle by showing the distance from center is equal to the radius.

Graph

The attachment shows a graph of the circle. Its equation is ...

(x -h)² +(y -k)² = r² . . . . . . for center (h, k) and radius r

We have (h, k) = (2, 13) and r = 5, so the equation is ...

(x -2)² +(y -13)² = 25 . . . . graphed equation

The point in question is also graphed, and is shown to lie on the circle.

Distance

If the given point satisfies the circle's equation, it lies on the circle.

For (x, y) = (-2, 10), we find ...

(-2 -2)² +(10 -13)² = (-4)² +(-3)² = 16 +9 = 25 . . . . . the equation is satisfied