If the tangents drawn from the point $(\lambda, 3)$ to the ellipse $\frac{x^2}{9} + \frac{y^2}{4} = 1$ are perpendicular to each other,then $\lambda = ......$

For the ellipse $\frac{x^2}{9} + \frac{y^2}{4} = 1$,a chord $PQ$ subtends a right angle at the center. What is the locus of the point of intersection of the tangents at $P$ and $Q$?

If a focal chord of the ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$ meets its minor axis at the point $(0,3)$,then the perpendicular distance from the centre of the ellipse to this focal chord is

If an ellipse with its axes as coordinate axes,$2a$ and $2b$ as the lengths of its major and minor axes respectively,passes through the points $(2,2)$ and $(3,1)$,then $3a^2+5b^2=$

If $4x - 3y - 5 = 0$ is a normal to the ellipse $3x^2 + 8y^2 = k$,then the equation of the tangent drawn to this ellipse at the point $(-2, m)$ $(m > 0)$ is

If the distance between a focus and the corresponding directrix of an ellipse is $8$ and the eccentricity is $1/2$,then the length of the minor axis is