AIEEE 2002 (Offline)Question 1
The pair of lines represented by $3ax^{2}+5xy+\left(a^{2}-2\right)y^{2}=0$ are perpendicular to each other for :
Points and Straight Lines
Solution
Perpendicular iff coefficient of $x^2$ + coefficient of $y^2=0$: $a^2+3a-2=0$, which has two real roots ($a=\frac{-3\pm\sqrt{17}}2$).