The equations of lines are given by  sinθx+a=1+cosθy, sinθx−a=−1−cosθy. The locus of point of intersection of lines is xm+yn=al then l+m+n is

Locus of point of intersection of two lines having parameter θ  , is the equation obtained by eliminating θ from both equations x+ay=1+cosθsinθ And x−ay=−1−cosθsinθ  Multiply both equationsx+ay⋅x−ay=−1+cosθsinθ⋅1−cosθsinθx2−a2y2=−1−cos2θsin2θ=−1x2−a2=−y2x2+y2=a2Here l=m=n=2 , Therefore, l+m+n=6