First slide

Pair of straight lines

Question

The tangent of the acute angle between the pair of lines $2 x^{2} - 3 xy + y^{2} = 0$ is

Easy

A

$\frac{1}{3}$
B

$\frac{1}{4}$
C

$\frac{1}{2}$
D

1

Solution

If $θ$ is acute angle between pair of lines represented by the equation ${ax}^{2} + 2 hxy + {by}^{2} = 0$ then $tanθ = \frac{2 \sqrt{h^{2} - ab}}{a + b}$
For the equation $2 x^{2} - 3 xy + y^{2} = 0$ ,the values are $a = 2, 2 h = - 3, b = 1$
Hence,
$\begin{matrix} tanθ = \frac{2 \sqrt{{(- \frac{3}{2})}^{2} - 2}}{3} \\ = \frac{1}{3} \end{matrix}$
Therefore, tangent of the acute angle between the pair of lines $2 x^{2} - 3 xy + y^{2} = 0$ ,is $\frac{1}{3}$

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