The equation of the ellipse whose one focus is at $(4, 0)$ and whose eccentricity is $4/5$, is
$\frac{{{x^2}}}{{{3^2}}} + \frac{{{y^2}}}{{{5^2}}} = 1$
$\frac{{{x^2}}}{{{5^2}}} + \frac{{{y^2}}}{{{3^2}}} = 1$
$\frac{{{x^2}}}{{{5^2}}} + \frac{{{y^2}}}{{{4^2}}} = 1$
$\frac{{{x^2}}}{{{4^2}}} + \frac{{{y^2}}}{{{5^2}}} = 1$
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.
The equation of an ellipse whose eccentricity is $1/2$ and the vertices are $(4, 0)$ and $(10, 0)$ is
The equation of the tangent at the point $(1/4, 1/4)$ of the ellipse $\frac{{{x^2}}}{4} + \frac{{{y^2}}}{{12}} = 1$ is
The line $12 x \,\cos \theta+5 y \,\sin \theta=60$ is tangent to which of the following curves?