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Prove that for all values of theta , the...

Prove that for all values of `theta` , the locus of the point of intersection of the lines `xcostheta+ysintheta=a` and `xsintheta-ycostheta=b` is a circle.

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Since the point of intersection satisfies both the given lines, we can find the locus by eliminating `theta` from the given equation. Therefore, by squaring and adding, we get equation
`x^(2)+y^(2)=a^(2)+b^(2)`
which is the equation of circle.
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