Eccentricity of Ellipse

Q.

Equation of the ellipse with vertices (-4, 3), (8, 3) and e=$\frac{5}{6}$ is

1. 

2. 

3. 

4. 

Q.

Equation of the ellipse with foci ($\pm ,0$) and e = $\frac{1}{4}$ is

1. 

2. 

3. 

4. 

Q.

The eccentricity of the ellipse which meets the straight line $\frac{x}{7}+\frac{y}{2}=1$ on the axis of x and the straight line $\frac{x}{3}-\frac{y}{5}=1$ on the axis of y and whose axes lie along the axes of coordinates, is

1. none of these

2. $\frac{3\sqrt{2}}{7}$

3. $\frac{2\sqrt{3}}{7}$

4. $\frac{\sqrt{3}}{7}$

Q.

The eccentricity of the ellipse $a{x}^2+b{y}^2+2fx+2gy+c=0$ if axis of ellipse parallel to x-axis is

1. $\left(\sqrt{\frac{b-a}{b}}\right)$

2. $\left(\sqrt{\frac{a+b}{a}}\right)$

3. none of these

4. $\left(\sqrt{\frac{a+b}{b}}\right)$

Q.

In an ellipse, if the lines joining a focus to the extremities of the minor axis make an equilateral triangle with the minor axis, the eccentricity of the ellipse is

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

2. $\frac{\sqrt{3}}{2}$

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

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

Q.

An ellipse has OB as a semi-minor axis. F and F' are its foci and the angle FBF' is a right angle. Then, the eccentricity of the ellipse is ___

1. $\frac{1}{\sqrt{2}}$

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

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

4. $\frac{1}{\sqrt{3}}$

Q. The ellipse $E_1:\frac{x^2}{9}+\frac{y^2}{4}=1$ is inscribed in a rectangle R whose sides are parallel to the coordinate axes. Another ellipse $E_2$ passing through the point (0, 4) circumscribes the rectangle R. The Eccentricity of the ellipse $E_2$ is

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

Q. The eccentricity of an ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,$whose latus rectum is half of its major axis, is .

1. $e=\frac{1}{\sqrt{2}}$
2. $e=\frac{1}{2}$
3. $e=\frac{1}{2\sqrt{2}}$
4. $e=\frac{1}{4}$

Q. The eccentricity of the ellipse $3x^2+2y^2=6$ is $\sqrt{3}$.

1. False
2. True

Q. If (3, 4) and (6, 8) are the foci of an ellipse passing through the Origin, then the eccentricity of the ellipse is

1. $\frac{1}{6}$
2. $\frac{1}{2}$
3. $\frac{1}{3}$
4. $\frac{1}{4}$