Maharashtra Board Solutions for Chapter: Conic Sections, Exercise 4: MISCELLANEOUS EXERCISE - 7

The line $y=mx+1$ is a tangent to the parabola $y^2=4x$ if $m$ is

The length of latus rectum of the parabola $x^2-4x-8y+12=0$ is 

If the focus of the parabola is $(0,–3)$ its directrix is $y=3$, then its equation is

The coordinates of a point on the parabola ${\mathrm{y}}^2=8\mathrm{x}$ whose focal distance is $4$ are 

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 $SP·S^{\text{'}}P=$