Question

A circle has center O(2, 3) and radius 5. Which of the following points is on the circle?

V(−1, −2)
X(5, −2)
Y(6, 0)
Z(6, 7)

Answer 1

To determine if a point is on a circle, calculate the distance between the point and the center and compare it to the radius.

Step-by-step explanation:

To determine whether a point is on a circle, you can calculate the distance between the center of the circle and the point and compare it to the radius. If the distance is equal to the radius, then the point lies on the circle. Using the distance formula, we can calculate the distance between the center of the circle O(2, 3) and each of the given points V(−1, −2), X(5, −2), Y(6, 0), and Z(6, 7).

For point V(−1, −2):

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

d = sqrt((-1 - 2)^2 + (-2 - 3)^2)

d = sqrt(9 + 25)

d = sqrt(34)

The distance is not equal to the radius of 5, so point V(−1, −2) is not on the circle.

Repeat this calculation for the other points to determine whether they lie on the circle.

Answer 2

equation of the circle:
(5)^2 = (x-2)^2 + (y-3)^2

see if any points work in the equation.

25 = (6-2)^2 + (0-3)^2
25 = 16 + 9
point (6,0) is on the circle