The equation of a curve in polar coordinates is $\frac{l}{r} = 2 \sin^2 \frac{\theta}{2}$. This equation represents:

If the tangent at a point $P$ on a parabola makes an angle $\alpha$ with its focal distance,then the angle between the tangent and the axis of the parabola is:

Let $y^{2}=12x$ be the parabola with its vertex at $O(0,0)$. Let $P$ be a point on the parabola and $A$ be a point on the $x$-axis such that $\angle OPA=90^{\circ}$. Then the locus of the centroid of such triangles $OPA$ is:

If a circle with its centre at the focus of the parabola $y^2 = 2px$ is such that it touches the directrix of the parabola,then a point of intersection of the circle and the parabola is

The length of the latus rectum of the parabola $20(x^2+y^2-6x-2y+10) = (4x-2y-5)^2$ is

Let a circle tangent to the directrix of a parabola $y^2 = 2ax$ have its center coinciding with the focus of the parabola. Then the points of intersection of the parabola and the circle are