First slide

Equation of line in Straight lines

Question

The locus of the point of intersection of the lines $x \sin θ + (1 - \cos θ) y = a \sin θ$ and $x \sin θ - (1 + \cos θ) y + a \sin θ = 0$ is

Moderate

A

$x^{2} - y^{2} = a^{2}$
B

$x^{2} + y^{2} = a^{2}$
C

$y^{2} = a x$
D

none of these

Solution

From the given equations we have
$\frac{1 - \cos θ}{\sin θ} = \frac{a - x}{y}$ and $\frac{1 + \cos θ}{\sin θ} = \frac{a + x}{y}$
Multiplying we get $\frac{1 - \cos^{2} θ}{\sin^{2} θ} = \frac{a^{2} - x^{2}}{y^{2}} \Rightarrow x^{2} + y^{2} = a^{2}$

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