Question

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

• A. two values of $a$
• B. for all $a$
• C. for one value of $a$
• D. for no values of $a$

Answer 1

The correct option is A two values of $a$

Using fact: Pair of lines $A{x}^2+2hxy+B{y}^2=0$ are

$\perp$ to each other if $A+B=0$

$\Rightarrow 3a+a^2-2=0$ $\Rightarrow a^2+3a-2=0$ $\Rightarrow$ There exist two value of a as $D>0$