First slide

Pair of straight lines

Question

If $θ$ is the acute angle between the pair of lines $x^{2} + 3 x y - 4 y^{2} = 0$ then $\sin θ =$

Moderate

A

$\frac{π}{6}$
B

$\frac{π}{3}$
C

$\frac{5}{\sqrt{34}}$
D

$\frac{3}{\sqrt{34}}$

Solution

$a = 1, b = - 4, 2 h = 3$
$\sin θ = \frac{2 \sqrt{h^{2} - a b}}{\sqrt{{(a - b)}^{2} + 4 h^{2}}} = \frac{5}{\sqrt{34}}$

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