The vertex of the parabola $(y - 2)^2 = 16(x - 1)$ is

If the tangents and normals at the extremities of a focal chord of a parabola $y^2 = 4ax$ intersect at $(x_1, y_1)$ and $(x_2, y_2)$ respectively,then:

The latus rectum of the conic passing through the origin and having the property that the normal at each point $(x, y)$ intersects the $x$-axis at $(x + 1, 0)$ is:

If the tangent to the parabola $y^2 = ax$ makes an angle of $45^{\circ}$ with the $x$-axis,then the point of contact is

The line $x - 1 = 0$ is the directrix of the parabola ${y^2} - kx + 8 = 0$. Then one of the values of $k$ is

Let the tangent to the parabola $S: y^{2}=2x$ at the point $P(2,2)$ meet the $x$-axis at $Q$ and the normal at $P$ meet the parabola $S$ at the point $R$. Then the area (in $sq. \ units$) of the triangle $PQR$ is equal to: