Parabola

- The locus of the mid-points of the line joining the focus and point on the parabola $y^{2}=4 a x$ is a parabola with the equation of directrix as

Locus of the poles of focal chord of a parabola is

An equilateral triangle is inscribed in the parabola $y^2=8 x$, with one of its vertices is the vertex of the parabola. Then, length of the side of that triangle is

If the focal chord drawn through the point $\mathrm{P}(5,5)$ to the parabola $\mathrm{y}^2=5 \mathrm{x}$ meets the parabola again at the point $\mathrm{Q}$, then the tangent drawn to this parabola at Q meets the axis of…

The number of normals drawn to the parabola $y^2=4 x$ from the point $(1,0)$ is

Match the points on the curve $2 y^2=x+1$ with the slopes of normals at those points and choose the correct answer.

If $P$ and the origin are the points of intersection of the parabolas $y^2=32 x$ and $2 x^2=27 y$; and if $\theta$ is the acute angle between these curves at $P$, then $5 \sqrt{\tan \theta}=$

If the tangent drawn to the parabola $y^2=4 x$ at $\left(t^2, 2 t\right)$ is the normal to the ellipse $4 x^2+5 y^2=20$ at $(\sqrt{5} \cos \theta, 2 \sin \theta)$, then

If the area bounded by the parabola \(y^2=16 a x\) and the line \(y=4 m x\) is \(\frac{a^2}{12}\) sq. units, then the value of ' \(m\) ' is

If the double ordinate of the parabola $y^2=8 x$ is of length 16 , then the angle subtended by it at the vertex of the parabola is

If a chord of the parabola $y^2=4 x$ passes through its focus and makes an angle $\theta$ with the $X$-axis, then its length is

If a perpendicular drawn through the vertex $O$ of the parabola $y^2=4 a x$ to any of its tangent meets the tangent at $N$ and the parabola at $M$, then $O N \cdot O M=$