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.

Explanation

To prove that the locus of the point of intersection of the lines \( x \cos \theta + y \sin \theta = a \) and \( x \sin \theta - y \cos \theta = b \) is a circle, we can follow these steps:

### Step 1: Set up the equations
Let the point of intersection be \( (h, k) \). Then we have the two equations:
1. \( h \cos \theta + k \sin \theta = a \) (Equation 1)
2. \( h \sin \theta - k \cos \theta = b \) (Equation 2)

### Step 2: Square both equations
...