In an ellipse,the distance between its foci is $6$ and the length of the minor axis is $8$. Then its eccentricity is

The eccentricity of the ellipse $x^2+4 y^2+2 x+16 y+13=0$ is

Let $e$ be the eccentricity of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$. If $a=5, b=4$ and the equation of the normal drawn at one end of the latus rectum that lies in the first quadrant is $lx+my=27$,then $l+m=$

The area of the region bounded by the curve $9x^2 + 4y^2 - 36 = 0$ is (in $\pi$)

Let $P \left(\frac{2 \sqrt{3}}{\sqrt{7}}, \frac{6}{\sqrt{7}}\right), Q, R$ and $S$ be four points on the ellipse $9x^2 + 4y^2 = 36$. Let $PQ$ and $RS$ be mutually perpendicular chords passing through the origin. If $\frac{1}{(PQ)^2} + \frac{1}{(RS)^2} = \frac{p}{q}$,where $p$ and $q$ are coprime,then $p+q$ is equal to $.........$.

$A$ man running on a racecourse notes that the sum of the distances from the two flag posts to him is always $10 \, m$ and the distance between the flag posts is $8 \, m$. Find the equation of the path traced by the man.