First slide

Pair of straight lines

Question

The angle between the pair of lines $x^{2} - 2 xysecα + y^{2} = 0$ is

Easy

A

$3 α$
B

$\frac{α}{2}$
C

$α$
D

$2 α$

Solution

If $θ$ is acute angle between pair of lines represented by the equation ${ax}^{2} + 2 hxy + {by}^{2} = 0$ then $cosθ = \frac{|a + b|}{\sqrt{{(a - b)}^{2} + {(2 h)}^{2}}}$
For the equation $x^{2} - 2 xysecα + y^{2} = 0$ , $a = 1, 2 h = - 2 secα, b = 1$
Hence,
$\begin{matrix} cosθ = \frac{2}{\sqrt{0 + 4 \sec^{2} α}} \\ = \frac{2}{2 secα} \\ = cosα \end{matrix}$
Therefore, $θ = α$

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