If two tangents drawn from a point $P$ to the parabola $y^{2}=16(x-3)$ are at right angles,then the locus of point $P$ is :

Find the equation of the parabola that satisfies the following conditions: Vertex $(0, 0)$,focus $(-2, 0)$.

If the normal drawn at the point $P(9, 9)$ on the parabola $y^2 = 9x$ meets the parabola again at $Q(a, b)$,then $2a + b =$

Three normals drawn from any point to the parabola $y^2 = 4ax$ cut the line $x = 2a$ in points whose ordinates are in arithmetical progression. Then the tangents of the angles which the normals make with the axis of the parabola are in:

$A$ beam is supported at its ends by supports which are $12 \, m$ apart. Since the load is concentrated at its centre,there is a deflection of $3 \, cm$ at the centre and the deflected beam is in the shape of a parabola. How far from the centre is the deflection $1 \, cm$?

The length of the chord of the parabola $x^2 = 4ay$ passing through its vertex and having slope $\tan\alpha$ is: