First slide

Pair of straight lines

Question

If the pair of lines $x^{2} cosθ + 3 xytanθ - y^{2} sinθ = 0$ are perpendicular to each other then $θ$

Easy

A

$\frac{π}{6}$
B

$\frac{π}{4}$
C

$\frac{π}{2}$
D

$\frac{π}{3}$

Solution

If the equation ${ax}^{2} + 2 hxy + {by}^{2} = 0$ represents a pair of perpendicular lines then $a + b = 0$
For the equation $x^{2} cosθ + 3 xytanθ - y^{2} sinθ = 0$
$a + b = cosθ - sinθ$
Equate to zero, and then find the suitable value for $θ$
It implies
$\begin{matrix} sinθ = cosθ \\ tanθ = 1 \\ θ = \frac{π}{4} \end{matrix}$
Therefore, the value of $θ$ is $\frac{π}{4}$

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