First slide

Pair of straight lines

Question

The angle between the pair of lines $(\cos^{2} θ) x^{2} + 2 xysinθ + (\sin^{2} θ - 1) = 0$ is

Moderate

A

$\frac{π}{2}$
B

$\frac{π}{3}$
C

$π$
D

$\frac{π}{4}$

Solution

The condition that two lines represented by the equation ${ax}^{2} + 2 hxy + {by}^{2} = 0$ are to be perpendicular is $a + b = 0$
For the equation $(\cos^{2} θ) x^{2} + 2 xysinθ + (\sin^{2} θ - 1) = 0$ , the values $a = \cos^{2} θ, b = \sin^{2} θ - 1$
Consider
$\begin{matrix} a + b = \cos^{2} θ + \sin^{2} θ - 1 \\ = 1 - 1 \\ = 0 \end{matrix}$
Since, $a + b = 0$ , the angle between the lines is $\frac{π}{2}$ .

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