First slide

Pair of straight lines

Question

The angle between the pair of lines $x^{2} + 4 xy + 2 y^{2} = 0$ is

Easy

A

$\sin^{- 1} (\frac{3}{\sqrt{17}})$
B

$\cos^{- 1} (\frac{3}{\sqrt{17}})$
C

$\cos^{- 1} (\frac{3}{17})$
D

$\sin^{- 1} (\frac{3}{17})$

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 $x^{2} + 4 xy + 2 y^{2} = 0$ , $a = 1, 2 h = 4, b = 2$
Hence,
$\begin{matrix} cosθ = \frac{3}{\sqrt{1 + 16}} \\ = \frac{3}{\sqrt{17}} \end{matrix}$
Therefore, $θ = \cos^{- 1} (\frac{3}{\sqrt{17}})$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App