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.

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 :

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

Locus of points of intersection of lines x=at^(2),y=2at

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

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)

If a+b+3c=0, c != 0 and p and q be the number of real roots of the equation ax^2 + bx + c = 0 belonging to the set (0, 1) and not belonging to set (0, 1) respectively, then locus of the point of intersection of lines x cos theta + y sin theta = p and x sin theta - y cos theta = q , where theta is a parameter is : (A) a circle of radius sqrt(2) (B) a straight line (C) a parabola (D) a circle of radius 2

The locus of lhe point of intersection of the lines x+4y=2a sin theta,x-y=a cos theta where theta is a variable parameter is