Question

Consider the family of lines 2x + y + 4 λ(x - 2y - 3) = 0 where λ is a parameter. Then, the number of lines belonging to this family whose distance from the point (2, -3) is √10 is

(A)   4

(B)  2

(C)  1

(D)  0

Answer 1

Correct option  (C)  1

Explanation :

The given family of lines can be written as

(2 + λ)x + (1 - 2λ)y + (4 - 3λ) = 0

By hypothesis, the distance of the line from (2, - 3) is

Hence, the required line is 3x - y + 1 = 0.