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

The length of the latus rectum of a parabola, whose vertex and focus are on the positive $x$-axis at a distance $R$ and $S(>R)$ respectively from the origin, is :

The axis of the parabola $y^2+2 x=0$ is

A tangent to the parabola $y^2 = 4x$ is inclined at an angle $45^{\circ}$ with the positive direction of $x$-axis. What is the point of contact of the tangent and the parabola?

What is the equation of parabola whose vertex is at $(0,0)$ and focus is at $(0,-2)$ ?

If $(2,3)$ is the vertex and.' $(3,2)$ is the focus of a parabola, then its equation is

For the parabola $y^2+6 y-2 x+5=0$, match the items in List-I with the suitable item in List-II given below: The correct matching is I $\quad$ II $\quad$ III $\quad$ IV

If the point $(a, 2 a)$ is an interior point of the region bounded by the parabola $y^2=16 x$ and the double ordinate through focus, then

If \(x+5=0\) is the directrix and \((-3,0)\) the vertex of a parabola, then equation of this parabola is ____

The number of normals drawn to the parabola $y^2=4 x$ from the point $(1,0)$ 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 focus of a parabola is $(0,-3)$ and its directrix is $y=3$, then it equation is