The eccentricity of the ellipse $9x^2 + 5y^2 - 18x - 2y - 16 = 0$ is

Assertion $(A)$: The length of the latus rectum of an ellipse is $4$. The focus and its corresponding directrix are respectively $(1, -2)$ and $3x + 4y - 15 = 0$. Then its eccentricity is $\frac{1}{2}$.
Reason $(R)$: The length of the perpendicular drawn from the focus of an ellipse to its corresponding directrix is $\frac{a(1 - e^2)}{e}$.
Which one of the following is correct?

The longest distance of the point $(a, 0)$ from the curve $2x^2+y^2=2x$ is

If the product of the lengths of the perpendiculars drawn from the foci to the tangent $y = \frac{-3}{4}x + 3\sqrt{2}$ of the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ is $9$,then the eccentricity of that ellipse is

$A$ line of fixed length $a + b$,where $a \neq b$,moves such that its ends are always on two fixed perpendicular straight lines. The locus of a point which divides the line into two parts of lengths $a$ and $b$ is

If the focal distance of an endpoint of the minor axis of an ellipse (taking its axes as the $x$ and $y$ axes respectively) is $k$ and the distance between its foci is $2h$,then its equation is: