The point of intersection of the normals to the parabola $y^2 = 4x$ at the ends of its latus rectum 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:

If the line $y=x$ is a tangent to the parabola $y=ax^{2}+bx+c$ at the point $(1,1)$ and the curve passes through $(-1,0)$, then

$A$ circle is drawn with its centre at the focus of the parabola $y^2 = 2px$ such that it touches the directrix of the parabola. Then a point of intersection of the circle and the parabola is

The axis of the parabola $9y^2 - 16x - 12y - 57 = 0$ is

The cable of a uniformly loaded suspension bridge hangs in the form of a parabola. The roadway which is horizontal and $100 \, m$ long is supported by vertical wires attached to the cable,the longest wire being $30 \, m$ and the shortest being $6 \, m$. Find the length of a supporting wire attached to the roadway $18 \, m$ from the middle. (in $, m$)