The locus of the point of intersection of lines xcos alpha + ysin alpha =a and xsin alpha - ycos alpha=b(alpha is a variable) is ________??

Let P(h, k) be the point of intersection of the given lines.

 

Then, hcos? + ksin? = a                                         … (1)

 

        hsin? – kcos? = b                                         … (2)

 

Here a is a variable. So we have to eliminate a.

 

Squaring and adding (1) and (2),

 

(hcos? + ksin?)² + (hsin? – kcos?)² = a² + b²

 

h² + k² = a² + b²

 

Hence, locus of (h, k) is x² + y² = a² + b².