Statement$-1$: If the distances of a point $\text{'}P\text{'}$ from the line $x+y+2=0$ and point $(3,4)$ are same then the locus of $\text{'}P\text{'}$ will be a parabola.

Statement$-2$: In $2$-dimensional geometry, if the distances of a point $\text{'}P\text{'}$ from a fixed line and a fixed point are same then the locus of $\text{'}P\text{'}$ will be a parabola.

A cable of a suspension bridge is in the form of a parabola whose span is $40$ metres. The road way is $5$ metres below the lowest point of the cable. An extra support is provided across the cable $30$ metres above the ground level. Find the length of the support if the height of the pillars are $55$ metres.$$