List of top Mathematics Questions on Ellipse asked in KEAM

If the distance between the foci of an ellipse is 4 and its eccentricity is $\frac{1}{2}$, then the length of its latus rectum is

If the foci of the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ coincide with the foci of the ellipse $\frac{x^2}{49} + \frac{y^2}{36} = 1$, then the value of $a^2 + b^2$ is equal to

If the eccentricity and the length of latus rectum of an ellipse are, respectively, \(\frac{1}{5}\) and \(\frac{48}{5}\), then the length of the major axis of the ellipse is

If the foci and vertices of an ellipse are respectively $(\pm 2,0)$ and $(\pm 3,0)$ then its eccentricity is

The line $x-y+4=0$ touches the ellipse $x^{2}+3y^{2}=12$ at ________.

The centre of the ellipse $4x^{2}+24x+9y^{2}-18y+9=0$ is ________.

The length of the latus rectum of the ellipse \[ \frac{x^2}{9}+\frac{y^2}{16}=1 \] is ________.

If the length of the latus rectum and the length of transverse axis of a hyperbola are \( 4\sqrt{3} \) and \( 2\sqrt{3} \) respectively, then the equation of the hyperbola is:

A point P on an ellipse is at a distance 6 units from a focus. If the eccentricity of the ellipse is \( \frac{3}{5} \), then the distance of P from the corresponding directrix is:

A point P on an ellipse is at a distance 6 units from a focus. If the eccentricity of the ellipse is \( \frac{3}{5} \), then the distance of P from the corresponding directrix is:

If the length of the latus rectum and the length of transverse axis of a hyperbola are \( 4\sqrt{3} \) and \( 2\sqrt{3} \) respectively, then the equation of the hyperbola is:

A point P on an ellipse is at a distance 6 units from a focus. If the eccentricity of the ellipse is \( \frac{3}{5} \), then the distance of P from the corresponding directrix is:

If the length of the latus rectum and the length of transverse axis of a hyperbola are \( 4\sqrt{3} \) and \( 2\sqrt{3} \) respectively, then the equation of the hyperbola is: