The end points of latus rectum of the parabola $y^2=24x$ are

Equation of the parabola with vertex at the origin and directrix $x+8=0$ is

The area of the triangle formed by the line joining the vertex of the parabola ${\mathrm{x}}^2=12\mathrm{y}$ to the end points of its latus rectum is

If $\mathrm{P}\left(\frac{\mathrm{\pi }}{4}\right)$ is any point on the ellipse $9{\mathrm{x}}^2+25{\mathrm{y}}^2=225$$S$and $S^{\text{'}}$ are it foci then $SP·S^{\text{'}}P=$

The equation of the parabola having $(2,4)$ and $(2,-4)$ as endpoints of its latus rectum is

If the parabola $y^2=4ax$ passes through $(3,2)$, then the length of its latus rectum (in units) is:

The equation of the ellipse having foci $(+4, 0)$ and eccentricity $\frac{1}{3}$ is,

The equation of a standard horizontal ellipse having eccentricity $\frac{\sqrt{3}}{2}$ and passing through $(-8, 3)$ is: