Question

The locus of the point of intersection of the lines x cos $\alpha +ysin\alpha =a$ and $xsin\alpha$ - y cos a = b, where $\alpha$ is parameter is

Answer 1

$xcos\alpha +ysin\alpha =a\times sin\alpha$

$\ominus \frac{xsin\alpha -ycos\alpha =b\times cos\alpha }{y(si{n}^2\alpha +co{s}^2\alpha )=asin\alpha -bcos\alpha }$

$\Rightarrow y=asin\alpha -bcos\alpha$

$xcos\alpha +ysin\alpha =a\times cos\alpha$

$\oplus \frac{xsin\alpha -ycos\alpha =b\times sin\alpha }{x(-co{s}^2\alpha +si{n}^2\alpha )=acos\alpha +bsin\alpha }$

$\Rightarrow x=acos\alpha +bsin\alpha$