The equation of the pair of straight lines perpendicular to the pair 2x2+3xy+2y2+10x+5y=0 and passing through the origin is

Question

The equation of the pair of straight lines perpendicular to the pair 2x2+3xy+2y2+10x+5y=0 and passing through the origin is (A)  2x2+5xy+2y2=0  (B)  2x2-3xy+2y2=0  (C)  2x2+3xy+y2=0  (D)  2x2-5xy+2y2=0

Tardigrade Admin · Accepted Answer

We know that equation of pair of straight line passing through the origin and perpendicular to ax2+2hxy+by2=0 is bx2-2hxy+ay2=0 ∴ Required equation of pair of straight line is 2x2-3xy+2y2=0

Q. The equation of the pair of straight lines perpendicular to the pair $2 x^{2} + 3 x y + 2 y^{2} + 10 x + 5 y = 0$ and passing through the origin is

$2 x^{2} + 5 x y + 2 y^{2} = 0$

$2 x^{2} - 3 x y + 2 y^{2} = 0$

$2 x^{2} + 3 x y + y^{2} = 0$

$2 x^{2} - 5 x y + 2 y^{2} = 0$

We know that equation of pair of straight line passing through the origin and perpendicular to
$a x^{2} + 2 h x y + b y^{2} = 0$
is $b x^{2} - 2 h x y + a y^{2} = 0$
$∴$ Required equation of pair of straight line is
$2 x^{2} - 3 x y + 2 y^{2} = 0$

Q. The equation of the pair of straight lines perpendicular to the pair 2x2+3xy+2y2+10x+5y=0 and passing through the origin is

2x2+5xy+2y2=0

2x2−3xy+2y2=0

2x2+3xy+y2=0

2x2−5xy+2y2=0