EXERCISE 7.1

Find the focal distance of a point on the parabola $y^2=16x$ whose ordinate is $2$ times the abscissa.

For the parabola $y^2=4x$, find the coordinate of the point whose focal distance is $17$.

Find the equation of the tangent to the parabola$\mathit{ }{y}^2 = 12x$ from the point $(2,5).$ 

Find the equation of the tangent to the parabola $y^2 = 36x$ from the point $(2,9).$ 

Two tangents to the parabola ${\mathrm{y}}^2 = 8\mathrm{x}$ meet the tangents at the vertex in the point $\mathrm{P}$ and $\mathrm{Q}.$ If $\mathrm{PQ}=4,$ prove that the equation of the locus of the point of intersection of two tangent is ${\mathrm{y}}^2 = 8(\mathrm{x} + 2).$

Find the equation of the common tangent to the parabola $y^2=4x$ and $x^2=32y$.

The tower of a 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 road way at the centre of the bridge, find the length of the vertical supporting cable from the centre.

A circle whose centre is $(4,-1)$, passes through the focus of the parabola $x^2+16y=0$. Show that the circle touches the directrix of the parabola.