Question

The pair of lines represented by $3a{x}^2+5xy+(a^2-2)y^2=0$ are perpendicular to each other for

• A. two real values of $a$
• B. infinitely many real values of $a$
• C. exactly one real value of $a$
• D. no real value of $a$

Answer 1

The correct option is A two real values of $a$

Perpendicularity condition : $\left(\text{coefficient of}{x}^2\right)+\left(\text{coefficient of}{y}^2\right)=0$
$\Rightarrow 3a+a^2-2=0$
$\Rightarrow a^2+3a-2=0$
$\Rightarrow a=\frac{-3\pm \sqrt{9+8}}{2}=\frac{-3\pm \sqrt{17}}{2}$