The tangents drawn at the extremities of a focal chord of the parabola $y^{2}=16x$:

If $a \neq 0$ and the line $2bx + 3cy + 4d = 0$ passes through the points of intersection of the parabolas $y^2 = 4ax$ and $x^2 = 4ay$,then

Which one of the following curves cuts the parabola $y^2 = 4ax$ at right angles?

The locus of the point of intersection of the tangents drawn at the ends of a focal chord of the parabola $x^{2}=-8y$ is

The two parabolas $y^2 = 4x$ and $x^2 = 4y$ intersect at a point $P$,whose abscissa is not zero,such that

Tangents are drawn at points $(x_i, y_i); i = 1, 2, 3$ lying on the parabola $y = x^2$ to enclose a triangle of area $\Delta$. If $x_1, x_2, x_3$ form an increasing arithmetic progression,where $x_1 = -1$ and $y_3 = 9$,then $\Delta$ is ............. $sq. \, units$.