Parabola

Equation of parabola having the extremities of its latus rectum as $\left(3,4\right)$ and $\left(4,3\right)$ is

If focus of a parabola is $\left(3,-4\right)$ and directrix is $x+y-2=0$, then its vertex is

An equilateral triangle $SAB$ is inscribed in the parabola $y^2=4ax$ having it's focus at $\text{'}\mathrm{S}\text{'}.$ If chord $AB$ lies towards the left of $S,$ then side length of this triangle is

Equation of parabola having its focus at $S\left(2,0\right)$ and one extremity of its Latus Rectum as $\left(2,2\right)$ is,

$AB$ is a chord of the parabola $y^2=4ax$ with vertex at $A$. If $BC$ is drawn perpendicular to $AB$ meeting the axis at $C$, then the projection of $BC$ on the $x-$ axis is

If $b$ and $c$ are the lengths of the segments of any focal chord of a parabola $y^2=4ax$ then, the length of the semi latus rectum is

The point $\left(2a,a\right)$ lies inside the region bounded by the parabola $x^2=4y$ and its latus rectum. Then

The locus of the mid-points of the focal chords of the parabola $y^2=4ax$ is another parabola whose vertex is given by

A parabola is drawn with its focus at $\left(3,4\right)$ and vertex at the focus of the parabola $y^2-12x-4y+4=0$. The equation of the parabola is

The locus of the mid-points of the focal chord of the parabola $y^2=4ax$ is

Find the length of intercept by the line $4y=3x-48$ on the parabola $y^2=64x$

Find the vertex of the parabola $x^2-8y-x+19=0$

The focal distance of a point on the parabola $y^2=12x$ is $4.$ Find the abscissa of this point.