What is the locus of the point of intersection of perpendicular tangents to the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$?

$A$ chord $PQ$ of the ellipse $\frac{x^2}{9} + \frac{y^2}{4} = 1$ subtends a right angle at its centre. The locus of the point of intersection of tangents drawn at $P$ and $Q$ is-

If a point $P(x, y)$ moves along the ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$ and if $C$ is the centre of the ellipse,then the sum of maximum and minimum values of $CP$ is

The equation $2x^2 + 3y^2 - 8x - 18y + 35 = k$ represents:

Find the equation of the ellipse $(a > b)$ whose distance between the foci is $8$ and the distance between the directrices is $18$.

The sum of the focal distances of any point on the conic $\frac{x^2}{25} + \frac{y^2}{16} = 1$ is