The length of the latus rectum of $x^2+3y^2=12$ is

The value of $\lambda$,for which the line $2x - \frac{8}{3}\lambda y = -3$ is a normal to the conic $x^2 + \frac{y^2}{4} = 1$ is

Let $p$ be the number of all triangles that can be formed by joining the vertices of a regular polygon $P$ of $n$ sides and $q$ be the number of all quadrilaterals that can be formed by joining the vertices of $P$. If $p+q=126$,then the eccentricity of the ellipse $\frac{x^2}{16}+\frac{y^2}{n}=1$ is :

For an ellipse $\frac{x^2}{9} + \frac{y^2}{4} = 1$ with vertices $A$ and $A'$,a tangent drawn at the point $P$ in the first quadrant meets the $y$-axis at $Q$,and the chord $A'P$ meets the $y$-axis at $M$. If $O$ is the origin,then $OQ^2 - MQ^2$ is equal to:

The area of the quadrilateral formed by drawing tangents at the ends of the latus recta of the ellipse $\frac{x^2}{4} + \frac{y^2}{1} = 1$ is

The sum of focal distances of any point on the ellipse with major and minor axes as $2a$ and $2b$ respectively,is equal to