The angle between the lines given by the equation a y^2+ (-1- ^2 … - Vidyadip

MCQ

The angle between the lines given by the equation $a y^2+\left(-1-\lambda^2\right) x y-a x^2=0$ is same as the angle between the lines

A
$5 x^2+2 x y-3 y^2=0$
B
$5 x^2+16 x y+5 y^2=0$
✓
$x y=0$
D
$x^2-2 x y-3 y^2=0$

✓

Answer

Correct option: C.

$x y=0$

(C) Given equation of pair of lines is $a y^2+\left(-1-\lambda^2\right) x y-a x^2=0$
$\therefore \quad A=-a, H=\frac{-1-\lambda^2}{2}, B=a$
$A+B=(-a)+a=0$
⇒ Angle between the given lines is $90^{\circ}$. Now, consider $x y=0$. Here, $A = B =0$
$\Rightarrow A+B=0$
$\therefore \quad$ The angle between the lines is $90^{\circ}$
$\therefore \quad$ Correct option is (C).

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