Latus Rectum of Ellipse

Q. The latusrectum LL’ subtends a right angle at the centre of the ellipse, then its eccentricity is

1. 
2. 
3. 
4. 

Q. Find the equation of the parabola that satisfies the following conditions: Vertex $(0,0)$ passing through $(5,2)$ and symmetric with respect to $y$- axis

Q. Find the equation for the ellipse that satisfies the given conditions: Length of major axis $26$, foci $(\pm 5,0).$

Q. Which of the following is INCORRECT about the ellipse $x^2+4y^2-2x-16y+13=0?$

1. The latus rectum of the ellipse is $1$
2. The distance between foci of the ellipse is $2\sqrt{3}$
3. Eccentricity of the ellipse is $\frac{\sqrt{3}}{2}$
4. Sum of the focal distances of a point $P(x,y)$ on the ellipse is $4\sqrt{3}$

Q. Find the equation of the hyperbola satisfying the give conditions: Vertices $(\pm 7,0)$
$e=\frac{4}{3}$

Q. Find the equation for the ellipse that given that satisfies the given conditions: Length of minor axis $16$, foci $(0,\pm 6).$

Q. Find the equation for the ellipse that satisfies the given conditions: Ends of major axis $(0,\pm \sqrt{5})$ ends of minor axis $(\pm 1,0).$

Q. Find the equation of the hyperbola satisfying the give conditions: Vertices $(0,\pm 5)$ foci $(0,\pm 8)$

Q. Find the equation for the ellipse that satisfies the given conditions: Ends of major axis $(\pm 3,0)$ ends of minor axis $(0,\pm 2).$

Q. For the horizontal ellipse, the difference between the length of the major axis and the latus rectum of an ellipse is

1. $ae$
2. $2ae$
3. $a{e}^2$
4. $2a{e}^2$

Q. Write the equations for the $x$-and $y$-axes.

Q.

The length of the latus rectum of the ellipse $5x^2+9y^2=45$ is

1. $\frac{\sqrt{5}}{4}$

2. $\frac{\sqrt{5}}{2}$

3. $\frac{5}{3}$

4. $\frac{10}{3}$

Q. Find the equation for the ellipse that satisfies the given conditions: Foci $(\pm 3,0),a=4.$

Q. If the length of the latus rectum of an ellipse is $4$ units and the distance between a focus and its nearest vertex on the major axis is $\frac{3}{2}$ units, then its eccentricity is

1. $\frac{2}{3}$
2. $\frac{1}{2}$
3. $\frac{1}{9}$
4. $\frac{1}{3}$

Q. Find the equation for the ellipse that satisfies the given conditions: Major axis on the $x$-axis, centre is origin and passes through the points $(4,3)$ and $(6,2).$

Q. If $\alpha$ and $\beta$ are the eccentric angles of the extremities of a focal chord of an ellipse, then the eccentricity of the ellipse is

1. 
2. 
3. 
4.