Question

Find the radius of the circle $(x\cos \alpha +y\sin \alpha -a{)}^2+(x\sin \alpha -y\cos \alpha -b{)}^2=k^2$ and if $\alpha$ varies, find the locus of its centre.

Answer 1

let us considered,

${\left(x\cos \alpha +y\sin \alpha -a\right)}^2+{\left(x\sin \alpha -y\cos \alpha -b\right)}^2=k^2$

$x\cos \alpha +y\sin \alpha -a=0$ and $x\sin \alpha -y\cos \alpha -b=0$ are two perpendicular lines

Hence,

These lines will represent diameter of circle.