Question

A circle has its center at the origin, and (5, -12) is a point on the circle. How long is the radius of the circle?

a) 5
b) 12
c) 13

Answer 1

Option C

The radius of circle is 13 units

Solution:

The equation of circle is given by formula:

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

Where, the center being at the point (h, k) and the radius being "r"

Given that circle has its center at the origin

(h, k) = (0, 0)

(5, -12) is a point on the circle

(x, y) = (5, 12)

Substituting in equation we get,

$(5-0)^2+(12-0)^2 = r^2\\\\5^2+12^2 = r^2\\\\r^2 = 5^2+12^2\\\\r^2 = 25 + 144\\\\r^2 = 169\\\\Taking\ square\ root\ on\ both\ sides\\\\r = \sqrt{169}\\\\r = \pm 13\\\\Since\ radius\ cannot\ be\ negative\ ignore\ r = -13\\\\Thus\ the\ solution\ is:\\\\ \r = 13$

Thus radius of circle is 13 units