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

The area of the rectangle formed by the perpendiculars from the centre of the standard ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ to the tangent and normal at its point whose eccentric angle is $\pi /4$ is:

The coordinates of the foci of the ellipse $3x^2 + 4y^2 - 12x - 8y + 4 = 0$ are

The locus of the mid-points of the chords of an ellipse $x^{2}+4y^{2}=4$ that are drawn from the positive end of the minor axis is

Find the coordinates of the foci,the vertices,the length of the major axis,the minor axis,the eccentricity,and the length of the latus rectum of the ellipse $\frac{x^{2}}{16} + \frac{y^{2}}{9} = 1$.

The tangent and normal to the ellipse $3x^2 + 5y^2 = 32$ at the point $P(2, 2)$ meet the $x$-axis at $Q$ and $R$,respectively. Then the area (in sq. units) of the triangle $PQR$ is