The number of values of a for which the pair of lines represented by 3ax2 + 5xy + (a2 -2)y2 = 0 are at right angles to each other , is

Question

The number of values of a for which the pair of lines represented by 3ax2 + 5xy + (a2 -2)y2 = 0 are at right angles to each other , is (A) 2 (B) 1 (C) infinitely many (D) 0

Tardigrade Admin · Accepted Answer

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

x^{2} +

Coefficient of

y^{2} = 0

\Rightarrow 3 a + a^{2} - 2 = 0

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

= \frac{- 3 \pm 17}{2}

Thus, there are two values.

Q. The number of values of a for which the pair of lines represented by 3ax2+5xy+(a2−2)y2=0 are at right angles to each other , is

2

1

infinitely many

0

The pair of lines represented by the given equation will be perpendicular to each other, if Coefficient of x2+ Coefficient of y2=0 ⇒3a+a2−2=0 ⇒a=2−3±9+8​​ =2−3±17​​ Thus, there are two values.

Q. 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

The pair of lines represented by the given equation will be perpendicular to each other,
if Coefficient of $x^{2} +$ Coefficient of $y^{2} = 0$
$\Rightarrow 3 a + a^{2} - 2 = 0$
$\Rightarrow a = \frac{- 3 \pm 9 + 8}{2}$
$= \frac{- 3 \pm 17}{2}$
Thus, there are two values.