The area of the triangle formed by the lines joining the vertex of the parabola $x^2=12y$ to the ends of its latus rectum is equal to $...$ sq. units.

$(1, 1)$ is the vertex and $x+y+1=0$ is the directrix of a parabola. If $(a, b)$ is its focus and $(c, d)$ is the point of intersection of the directrix and the axis of the parabola,then $a+b+c+d=$

If the line $2x - 3y = k$ is tangent to the parabola $y^2 = 6x$,then what is the value of $k$?

What is the equation of the pair of tangents drawn from the point $(1, 4)$ to the parabola $y^2 = 12x$?

The length of the chord of the parabola $y^2 = 4ax$ which passes through the vertex and makes an angle $\theta$ with the axis of the parabola is:

The angle between tangents to the parabola $y^2 = 4ax$ at the points where it intersects with the line $x - y - a = 0$ is