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

Answer 1

The correct option is A two values of $a$

$3a{x}^2+5xy+(a^2-2)y^2=0$ are perpendicular to each other

$\therefore$ coefficient of $x^2+$coefficient of $y^2=0$

$\Rightarrow 3a+a^2-2=0$

$\Rightarrow a^2+3a-2=0$

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

so $a=\frac{-3+\sqrt{17}}{2}$ and $a=\frac{-3-\sqrt{17}}{2}$