Locus of point of intersection of the lines `xsin theta- y cos theta = 0` and `ax sec theta- by cosec theta = a^2-b^2`

Locus of point of intersection of the lines x sin theta-y cos theta=0 and ax sec theta-by cos ec theta=a^(2)-b^(2)

Locus of point of intersection of the lines x sin theta-y cos theta=0 and ax sec theta-by cos ec theta=a^(2)-b^(2)

The locus of the point of intersection of the lines ax sec theta+by tan theta=a and ax tan theta+by sec theta=b is

The locus of the points of intersection of the lines x cos theta+y sin theta=a and x sin theta-y cos theta=b , ( theta= variable) is :

Prove that for all values of theta ,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.

For different values of theta, the locus of the point of intersection of the straight lines x sin theta-y(cos theta-1)=a sin theta and x sin theta-y(cos theta+1)+a sin theta=0 represents

The equation of the locus of the point of intersection of the straight lines x sin theta+(1-cos theta)y=a sin theta and x sin theta-(1-cos theta)y+a sin theta=0 is

If 2y cos theta= xsin theta and 2x sec theta-y cosec theta=3 then x^2/4+y^2=

If 2y cos theta =x sin theta and 2x sec theta -y cosec theta =3, then x ^(2) +4y^(2)=