For all values of $θ$ , the locus of the point of intersection of the lines $x c o s θ + y s i n θ = a$ and $x s i n θ - y c o s θ = b$ 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
The point of intersection is $x = a c o s θ + b s i n θ$
$y = a s i n θ - b c o s θ$ .
Therefore, $x^{2} + y^{2} = a^{2} + b^{2}$ .
Obviously, it is equation of a circle.

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