Question

Let a circle with centre at C be made to pass through the point P(1,2), touching the straight lines 7x - y = 5 and x + y + 13 = 0 at A and B respectively. If tangents at A and B intersect at Q, then

(A) area of quadrilateral ACBQ can be 100 sq. units

(B) radius of circle can be √40

(C) area of quadrilateral ACBQ can be 200 sq. units

(D) radius of circle can be 10

Answer 1

Correct option (A) area of quadrilateral ACBQ can be 100 sq. units

Explanation:

Clearly, the point lies on 7x - y = 5

Also, centre of the circle must lie on the bisectors of the lines x + y + 13 = 0 and 7x - y - 5 = 0 given by

Let (h,k) be the centre of the circle, then h -3k = 35 ..... (1) and 3h + k +15 = 0 ..... (2)

Clearly CA is perpendicular AQ

Therefore area of quadrilateral ACBQ

units = 100 sq. units. Hence (A)