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

Question

Aicharya · Accepted Answer

The pair of the lines represented by the given equation will be perpendicular to each other, when

Coefficient of $x^{2} +$ coefficient of $y^{2} = 0$

$3 a + a^{2} - 2 = 0$

On solving the above quadratic equation,

$a = \frac{- 3 \pm \sqrt{17}}{2}$

There are two values.

The number of values of a for which the pair of lines represented by 3 a x 2 + 5 x y + a 2 - 2 y 2 = 0 are…