If the length of the major axis of an ellipse is three times the length of its minor axis, then its eccentricity is
$\frac{1}{3}$
$\frac{1}{{\sqrt 3 }}$
$\frac{1}{{\sqrt 2 }}$
$\frac{{2\sqrt 2 }}{3}$
A man running a racecourse notes that the sum of the distances from the two flag posts from him is always $10 \,m$ and the distance between the flag posts is $8\, m$ Find the equation of the posts traced by the man.
An ellipse with its minor and major axis parallel to the coordinate axes passes through $(0,0),(1,0)$ and $(0,2)$. One of its foci lies on the $Y$-axis. The eccentricity of the ellipse is
If the co-ordinates of two points $A$ and $B$ are $(\sqrt{7}, 0)$ and $(-\sqrt{7}, 0)$ respectively and $P$ is any point on the conic, $9 x^{2}+16 y^{2}=144,$ then $PA + PB$ is equal to
The equation of normal at the point $(0, 3)$ of the ellipse $9{x^2} + 5{y^2} = 45$ is
The eccentricity of the ellipse ${\left( {\frac{{x - 3}}{y}} \right)^2} + {\left( {1 - \frac{4}{y}} \right)^2} = \frac{1}{9}$ is