Question

Equation $x^{2}+k_{1} y^{2}+2 k_{2} y=a^{2}$ represents a pair of perpendicular straight lines if

• A. $k _{1}=1, k _{2}= a$
• B. $k _{1}=1, k _{2}=- a$
• C. $k _{1}=-1, k _{2}=- a$
• D. $k _{1}=-1, k _{2}= a$

Answer 1

Answer: (C), (D)

Lines are perpendicular if $1+ k _{1}=0$
Also for pair of straight line,
$ ABC +2 FGH - AF ^{2}- BF ^{2}- CH ^{2}=0$
$\Rightarrow k _{1}=-1 $ and $ k _{2}=\pm a$