If the focus of a parabola is $(0,-3)$ and its directrix is $y=3$,then its equation is

If two circles $x^2+y^2-6x-6y+13=0$ and $x^2+y^2-8y+9=0$ intersect at $A$ and $B$,then the focus of the parabola whose directrix is the line $AB$ and vertex is the point $O(0,0)$ is

If the straight line $y=mx+c$ is parallel to the axis of the parabola $y^2=lx$ and intersects the parabola at $\left(\frac{c^2}{8}, c\right)$,then the length of the latus rectum is

Find the length of the chord of the parabola $y^2 = 4x$ which passes through the vertex and makes an angle of $30^{\circ}$ with the $x$-axis. (in $\sqrt{3}$)

The point of intersection of the normals to the parabola $y^2 = 4x$ at the ends of its latus rectum is

What is the angle in degrees between the tangents drawn from the origin to the parabola $y^2 = 4a(x - a)$?