Question

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

• A. $ 2{{x}^{2}}+5xy+2{{y}^{2}}=0 $
• B. $ 2{{x}^{2}}-3xy+2{{y}^{2}}=0 $
• C. $ 2{{x}^{2}}+3xy+{{y}^{2}}=0 $
• D. $ 2{{x}^{2}}-5xy+2{{y}^{2}}=0 $

Answer 1

Answer: (B)

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