If the normal chord drawn at $(2 a, 2 a \sqrt{2})$ on the parabola $y^2=4 a x$ subtends an angle $\theta$ at its vertex,then $\theta=$ (in $^{\circ}$)

The shortest distance between the line $y - x = 1$ and the curve $x = y^2$ 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 $, m$)

Find the equation of the normal to the curve $x^{2}=4y$ which passes through the point $(1,2)$.

The locus of the midpoints of the chords of the parabola $y^2 = 4ax$ which pass through the origin is:

The length of the latus rectum of the parabola $x^{2}+2y=8x-7$ is