Find the radius of the circle `(xcosalpha+ysinalpha-a)^2+(xsinalpha-ycosalpha-b)^2=k^2,ifalpha` varies, the locus of its centre is again a circle. Also, find its centre and radius.

Explanation

To solve the problem, we need to analyze the given equation of the circle and find the radius, center, and the locus of its center as alpha varies.

### Step-by-Step Solution:

1. **Given Equation**:
The equation of the circle is given as:
\[
(x \cos \alpha + y \sin \alpha - a)^2 + (x \sin \alpha - y \cos \alpha - b)^2 = k^2
...