If pairs of straight lines x2-2 p x y-y2=0 and x2-2 q x y-y2=0 be such that pair bisects the angle between the other pair, then

Question

If pairs of straight lines x2-2 p x y-y2=0 and x2-2 q x y-y2=0 be such that pair bisects the angle between the other pair, then (A) p q=1 (B) p q=2 (C) p q=-2 (D) p q=-1

Tardigrade Admin · Accepted Answer

Equation of angle bisector for a x2+2 h x y +b y2=0 ⇒ (x2-y2/a-b)=(x y/h) and for x2-2 p x y-y2=0 ⇒ (x2-y2/1-(-1))=(x y/-p) ⇒ x2-y2+(2 x y/p)=0 Given equation of angle bisector is x2-2 q x y +y2=0 On comparing ⇒ (2/P)=-2 q ⇒ p q=-1

Q. If pairs of straight lines $x^{2} - 2 p x y - y^{2} = 0$ and $x^{2} - 2 q x y - y^{2} = 0$ be such that pair bisects the angle between the other pair, then

$pq = 1$

$pq = 2$

$pq = - 2$

$pq = - 1$

Q. If pairs of straight lines x2−2pxy−y2=0 and x2−2qxy−y2=0 be such that pair bisects the angle between the other pair, then

pq=1

pq=2

pq=−2

pq=−1

Equation of angle bisector for ax2+2hxy+by2=0 ⇒a−bx2−y2​=hxy​ and for x2−2pxy−y2=0 ⇒1−(−1)x2−y2​=−pxy​ ⇒x2−y2+p2xy​=0 Given equation of angle bisector is x2−2qxy+y2=0 On comparing ⇒P2​=−2q ⇒pq=−1

Q. If pairs of straight lines $x^{2} - 2 p x y - y^{2} = 0$ and $x^{2} - 2 q x y - y^{2} = 0$ be such that pair bisects the angle between the other pair, then

$pq = 1$

$pq = 2$

$pq = - 2$

$pq = - 1$