Question

The number of values of $a$ for which the pair of lines represented by
$3ax^2 + 5xy + (a^2 -2)y^2 = 0 $ are at right angles to each other , is

• A. 2
• B. 1
• C. infinitely many
• D. 0

Answer 1

Answer: (A)

The pair of lines represented by the given equation will be perpendicular to each other,
if Coefficient of $x^{2}+$ Coefficient of $y^{2}=0$
$\Rightarrow 3 a+a^{2}-2=0$
$\Rightarrow a=\frac{-3 \pm \sqrt{9+8}}{2}$
$=\frac{-3 \pm \sqrt{17}}{2}$
Thus, there are two values.