Question

The radius of the circle which passes through the point (2, 3) and touches the line 2x -3y -13 = 0 at the point (2, 3) is

(a) 2√2

(b) √8

(c) √13

(d) 2√3

Answer 1

Correct option (b) √8

Explanation :

Let (2,3) and (2,-3) Let M be the midpoint of AB = (2 ,0) and C be the centre of the circle (see Fig). Therefore, C is the intersection of the lines CB and CM. Equation of the line CM is

y = 0 ...(1)

Equation of the line CB is

y + 3 = -3/2(x - 2)

That is, 3x + 2y = 0 ...(2)

Equations (1) and (2) imply that the centre of the circle is (0, 0). Therefore, the radius of the circle is