First slide

Pair of straight lines

Question

If the pair of lines given by $(x^{2} + y^{2}) \sin^{2} α = {(x C o s α - y S i n α)}^{2}$ are perpendicular to each other then $α =$

Moderate

A

$\frac{π}{2}$
B

0
C

$\frac{π}{4}$
D

$\frac{π}{3}$

Solution

$a = \sin^{2} α - \cos^{2} α$
$b = \sin^{2} α - \sin^{2} α = 0$
$a + b = 0, α = \frac{π}{4}$

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