If the line $lx + my + n = 0$ is tangent to the parabola $y^{2} = 4ax$,then

Let $L_{1}$ be a tangent to the parabola $y^{2}=4(x+1)$ and $L_{2}$ be a tangent to the parabola $y^{2}=8(x+2)$ such that $L_{1}$ and $L_{2}$ intersect at right angles. Then $L_{1}$ and $L_{2}$ meet on the straight line

What are the coordinates of the endpoints of the latus rectum of the parabola $(y - 1)^2 = 4(x + 1)$?

Let the image of the parabola $x^{2} = 4y$ in the line $x - y = 1$ be $(y + a)^{2} = b(x - c)$, where $a, b, c \in \mathbb{N}$. Then $a + b + c$ is equal to

The equation of a parabola which passes through the intersection points of the straight line $x + y = 0$ and the circle $x^2 + y^2 + 4y = 0$ is:

The equation of the tangent to the parabola $y^2 = 4x + 5$ parallel to the line $y = 2x + 7$ is