The length of the latus rectum of the parabola $4y^2 + 2x - 20y + 17 = 0$ is

What is the focus of the parabola $y^2 - x - 2y + 2 = 0$?

Let the length of the focal chord $PQ$ of the parabola $y^2=12x$ be $15$ units. If the distance of $PQ$ from the origin is $p$,then $10p^2$ is equal to:

What is the area of the triangle formed by the vertex of the parabola $x^2 = 12y$ and the endpoints of its latus rectum (in square units)?

Tangent and normal are drawn at $P(16, 16)$ on the parabola ${y^2} = 16x$,which intersect the axis of the parabola at $A$ and $B$,respectively. If $C$ is the centre of the circle through the points $P, A$ and $B$ and $\angle CPB = \theta$,then a value of $\tan \theta$ is:

If $2x + 3y + 12 = 0$ and $x - y + 4\lambda = 0$ are conjugate with respect to the parabola $y^2 = 8x$,then $\lambda$ is equal to