The equation of the tangent to the parabola $y^2 = 16x$,which is perpendicular to the line $y = 3x + 7$,is

Find the length of the chord intercepted by the line $4y = 3x - 48$ on the parabola $y^{2} = 64x$.

Let $A_1, B_1, C_1$ be three points in the $xy$-plane. Suppose that the lines $A_1 C_1$ and $B_1 C_1$ are tangents to the curve $y^2=8x$ at $A_1$ and $B_1$,respectively. If $O=(0,0)$ and $C_1=(-4,0)$,then which of the following statement$(s)$ is (are) $TRUE$?
$(A)$ The length of the line segment $OA_1$ is $4\sqrt{3}$
$(B)$ The length of the line segment $A_1 B_1$ is $16$
$(C)$ The orthocenter of the triangle $A_1 B_1 C_1$ is $(0,0)$
$(D)$ The orthocenter of the triangle $A_1 B_1 C_1$ is $(1,0)$

From the point $(-1, -6)$, two tangents are drawn to the parabola $y^2 = 4x$. The angle between the two tangents is:

The parabola with directrix $x+2y-1=0$ and focus $(1,0)$ is

If the tangents of the parabola $y^2=8x$ passing through the point $P(1,3)$ touch the parabola at $A$ and $B$,then the area (in sq. units) of $\triangle PAB$ is