Q120 / 225 · JEE Main 2002 · Mathematics

The point of lines represented by $3 a x^2+5 x y+\left(a^2-2\right) y^2=0$ and perpendicular to each other for

Correct answer
A
two values of a
B
$\forall a$
C
for one value of a
D
for no values of a

Solution

$3 a+a^2-2=0 \Rightarrow a^2+3 a-2=0 \Rightarrow a=\frac{-3 \pm \sqrt{9+8}}{2}=\frac{-3 \pm \sqrt{17}}{2}$

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

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