For all values of $θ$ the locus of the point of intersection of the lines x cos $θ$ + y sin $θ$ = a and x sin $θ$ - y cos $θ$ =b is

An ellipse

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A circle

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A parabola

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A hyperbola

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Solution

The correct option is B
A circle

$x c o s θ + y s i n θ = a 1$
$x s i n θ - y c o s θ = b 2$
Squaring and adding 1 and 2 we get
$x^{2} + y^{2} = a^{2} + b^{2}$

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