If a chord of the circle is trisected at the points and

MATHEMATICS · Single correct · A Level · Mathematics · Coordinate geometry in the (x y) plane · Coordinate geometry in the (x y) plane

Problem

If a chord of the circle

x^2 + y^2 - 4x - 2y - c = 0

is trisected at the points

\left(\frac{1}{3}, \frac{1}{3}\right)

and

\left(\frac{8}{3}, \frac{8}{3}\right)

, then (1)

c = 10

(2)

c = 20

(3)

c = 15

(4)

c^2 - 40c + 400 = 0