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 ________.
Find the center of the ellipse given by the equation \[ 4x^2 + 24x + 9y^2 - 18y + 9 = 0 \]
Length of latus rectum of ellipse \[ \frac{x^2}{9} + \frac{y^2}{16} = 1 \]
The length of the minor axis of the ellipse with foci \( (\pm 2, 0) \) and eccentricity \( \frac{1}{3} \) is:
The eccentricity of an ellipse is \( \frac{1}{3} \) and its center is at the origin. If one of the directrices is \( x = 9 \), then the equation of the ellipse is:
The eccentricity of the ellipse \[ p x^2 + 5y^2 = 80, \quad \text{where } p > 5, \] is \( \frac{\sqrt{3}}{2} \). Then the value of \( p \) is
For an ellipse, the foci are \( F(3,0) \) and \( F'(-3,0) \). If the length of the minor axis is 8, then the length of the major axis is equal to
The eccentricity of the ellipse \(\frac{x^2}{36}+\frac{y^2}{16}=1\) is
Eccentricity of the ellipse $4x^2 + y^2 -8x + 4y -8= 0$ is
The equation $5x^2 + y^2 + y = 8$ represents
The eccentricity of the ellipse $ \frac{\left(x-1\right)^{2}}{2} + \left(y + \frac{3}{4}\right)^{2} = \frac{1}{16}$ 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:
If the semi-major axis of an ellipse is 3 and the latus rectum is $\frac{16}{9},$ then the standard equation of the ellipse is
If the straight line $y = 4x + c$ touches the ellipse $\frac{x^2}{4} + y^2 = 1 $ then c is equal to