Ellipse - Coordinate Geometry - Mathematics Previous Year Questions

The length of the latusrectum of an ellipse is $\frac{18}{5}$ and eccentricity is $\frac{4}{5}$, then equation of the ellipse is .....

The eccentricity of the ellipse \(y^2+4 x^2-12 x+6 y+14=0\) is

A rectangle of maximum area is inscribed in an ellipse \(\frac{x^2}{25}+\frac{y^2}{16}=1\), then its dimensions are

The eccentricity of the ellipse $9 x^2+5 y^2-30 y=0$ is

AOB is the positive quadrant of the ellipse $\frac{x^2}{25}+\frac{y^2}{9}=1$ in which $\mathrm{OA}=5, \mathrm{OB}=3$. The area between the arc AB and the chord AB of the ellipse in sq. units is

The equations of two ellipses are $\frac{x^2}{4}+\frac{y^2}{2}=1$ and $\frac{x^2}{36}+\frac{y^2}{\mathrm{~b}^2}=1$. If the product of their eccentricities is $\frac{\sqrt{2}}{3}$, then the product of the length of the major axis and minor axis of the second ellipse is

The foci of the conic $25 x^2+16 y^2-150 x=175$ are

The eccentricity of the curve represented by $x=3(\cos t+\sin t), y=4(\cos t-\sin t)$ is

The tangent to the ellipse $9 x^2+16 y^2=288$ making equal intercepts on the co-ordinate axes intersects the X -axis and the Y -axis in the points $A$ and $B$ respectively. Then $A(\triangle O A B)=$ (where O is origin)

The eccentric angle of the point $\mathrm{P}(-6,2)$ of the ellipse $\frac{x^2}{48}+\frac{y^2}{16}=1$ is