The position of the point $(4, -3)$ with respect to the ellipse $2x^2 + 5y^2 = 20$ is

Let $P$ and $Q$ be the foci of an ellipse and let $R$ be one end of its minor axis. If $\triangle PQR$ is an equilateral triangle,then the eccentricity of the ellipse is equal to

The length of the latus rectum of $16x^2 + 25y^2 = 400$ is

The curve represented by $x = 5(\cos t + \sin t)$ and $y = 3(\cos t - \sin t)$ is (where $t$ is a parameter):

Let $f$ be a strictly decreasing function defined on $\mathbb{R}$ such that $f(x) > 0, \forall x \in \mathbb{R}$. Let $\frac{x^2}{f(a^2+5a+3)} + \frac{y^2}{f(a+15)} = 1$ be an ellipse with the major axis along the $y$-axis. The value of $a$ can lie in the interval$(s)$:

Find the equation of the chord of the ellipse $2x^2 + 5y^2 = 20$ which is bisected at the point $(2, 1)$.