The equation of the parabola with $x+2y=1$ as directrix and $(1,0)$ as focus is

If the length of the latus rectum of a parabola,whose focus is $(a, a)$ and the tangent at its vertex is $x+y=a$,is $16$,then $|a|$ is equal to.

If the normal to the parabola $y^2=4x$ at $P(1,2)$ meets the parabola again at $Q$,then the coordinates of $Q$ are

If $mx - y + c = 0$ is a normal at a point $P$ on the parabola $y^2 = 16x$ and the focal distance of $P$ is $40$ units,then $|c| =$

What do the equations $x = \frac{t}{4}$ and $y = \frac{t^2}{4}$ represent?

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 $, m$)