Question

If x² – 2pxy – y² = 0 and x² – 2qxy – y^{2 =} 0 represent a pair of lines (p ≠ q) such that each pair bisects the angle between the other, then

(a)  pq = 1

(b)  pq = -1

(c)  1/p + 1/q = 1

(d)  1/p + 1/q = 1/2

Answer 1

Correct option  (b) pq = -1

Explanation

the equation of the pair of angle bisector of the lines x² – 2pxy – y² = 0 is

 However, by hypothesis, x² -  2qxy - y² = 0 is the pair of angle bisectors. Therefore,

p/1 = 2/-2q = -p/-1 pq = -1