M L Aggarwal Solutions for Chapter: Conic Sections, Exercise 3: EXERCISE

 An arc is in the form of a parabola with its axis vertical. The arc is $10 \mathrm{m}$ high and $5 \mathrm{m}$ wide at the base. $\sqrt{k}$ wide  is $2 \mathrm{m}$ from the vertex of the parabola. Find $k$.

The towers of a suspension bridge, hung in the form of a parabola, have their tops $30$ meters above the roadway and are $200$ meters apart. If the cable is $5$ meters above the roadway at the centre of the bridge, find the length of the vertical (in meters) supporting cable $30$ meters from the centre.

The girder of a railway bridge is a parabola with its vertex at the highest point, $15$ metres above the ends. If the span is $150$ metres, find its height( in meters ) at $30$ metres from the mid-point.