Q86 / 160 · AP EAMCET 2021 (19 Aug Shift 1) · Mathematics

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 though the origin is______

Solution

Given equation of Pair of straight lines $2 x^{2} + 3 x y + 2 y^{2} + 10 x +$ $5 y = 0$

It is in the form of $a x^{2} + 2 h x y + b y^{2} + 2 g x + 2 f y + c = 0$

Here $a = 2, h = \frac{3}{2}, b = 2 .$

Equation perpendicular to given Pair of straight lines passing through origin is

$b x^{2} - 2 h x y + a y^{2} = 0$

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

Hence, the correct answer is option: 'B'.