If the centre, one of the foci and semi-major axis of an ellipse be $(0, 0), (0, 3)$ and $5$ then its equation is
$\frac{{{x^2}}}{{16}} + \frac{{{y^2}}}{{25}} = 1$
$\frac{{{x^2}}}{{25}} + \frac{{{y^2}}}{{16}} = 1$
$\frac{{{x^2}}}{9} + \frac{{{y^2}}}{{25}} = 1$
None of these
The equation of the ellipse whose one focus is at $(4, 0)$ and whose eccentricity is $4/5$, is
The line $lx + my - n = 0$ will be tangent to the ellipse $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$, if
Let $P$ be a variable point on the ellipse $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$ with foci ${F_1}$ and ${F_2}$. If $A$ is the area of the triangle $P{F_1}{F_2}$, then maximum value of $A$ is
The position of the point $(1, 3)$ with respect to the ellipse $4{x^2} + 9{y^2} - 16x - 54y + 61 = 0$
If the line $x\cos \alpha + y\sin \alpha = p$ be normal to the ellipse $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$, then