If the axis of a parabola is horizontal and it passes through the points $(0, 0), (0, -1)$ and $(6, 1)$,then its equation is

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

The locus of a point which divides the line segment joining the focus and any point on the parabola $y^2 = 12x$ in the ratio $m:n$ $(m+n \neq 0)$ is a parabola. Then the length of the latus rectum of that parabola is

The tangents to the curve $y = (x - 2)^2 - 1$ at its points of intersection with the line $x - y = 3$ intersect at the point:

What is the area of the triangle formed by the tangents drawn from the point $(4, 6)$ to the parabola $y^2 = 8x$ and their chord of contact?

Find the equation of the common tangent to the parabolas $y^2 = 2x$ and $x^2 = 16y$.