The equation of a tangent to the parabola $y^2 = 8x$ is $y = x + 2$. The point on this line from which the other tangent to the parabola is perpendicular to the given tangent is

The equation of the line passing through the point $(1/2, 2)$ and tangent to the parabola $y = -\frac{x^2}{2} + 2$ and secant to the curve $y = \sqrt{4 - x^2}$ is

If $(x_1, y_1)$ and $(x_2, y_2)$ are the points on the parabola $y^2 = 32x$ each at a focal distance of $10$ units,then $2(x_1^2 + x_2^2 + y_1^2 + y_2^2) = $

The line $y = mx + c$ touches the parabola $x^2 = 4ay$ if:

If the tangents at the endpoints $P$ and $Q$ of a chord of a parabola meet at point $T$,then the distances of points $P, T, Q$ from the focus of the parabola are in which progression?

Let $P$ represent the point $(3, 6)$ on the parabola $y^2 = 12x$. For the parabola $y^2 = 12x$,if $l_1$ is the length of the normal chord drawn at $P$ and $l_2$ is the length of the focal chord drawn through $P$,then $\frac{l_1}{l_2} = $