In an ellipse, the distance between its foci is $6$ and minor axis is $8.$ Then its eccentricity is :
$\frac{3}{5}$
$\frac{1}{2}$
$\frac{4}{5}$
$\frac{1}{\sqrt 5}$
The equation of the normal at the point $(2, 3)$ on the ellipse $9{x^2} + 16{y^2} = 180$, is
The eccentricity of the ellipse $4{x^2} + 9{y^2} + 8x + 36y + 4 = 0$ is
An arch is in the form of a semi-cllipse. It is $8 \,m$ wide and $2 \,m$ high at the centre. Find the height of the arch at a point $1.5\, m$ from one end.
If the length of the minor axis of ellipse is equal to half of the distance between the foci, then the eccentricity of the ellipse is :
The ellipse $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$ and the straight line $y = mx + c$ intersect in real points only if