Double Ordinate of Hyperbola

Q. If PQ is a double ordinate of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ such that OPQ is an equilateral triangle, O being the centre of the hyperbola. Then the eccentricity e of the hyperbola, satisfies

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

Q.

If AB is a double ordinate of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ such that $\Delta OAB$ is an equilateral triangle O being the origin, then the eccentricity of the hyperbola satisfies

1. e > $\sqrt{3}$

2. 1 < e < $\frac{1}{\sqrt{3}}$

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

4. e > $\frac{2}{\sqrt{3}}$

Q. If PQ is a double ordinate of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$such that OPQ is an equilateral triangle, O being the centre of the hyperbola. Then, the eccentricity e of the hyperbola satisfies

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

Q.

If AB is a double ordinate of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ such that $\Delta OAB$ is an equilateral triangle O being the origin, then the eccentricity of the hyperbola satisfies

1. e > $\sqrt{3}$

2. 1 < e < $\frac{1}{\sqrt{3}}$

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

4. e > $\frac{2}{\sqrt{3}}$

Q. If PQ is a double ordinate of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ such that OPQ is an equilateral triangle, O being the centre of the hyperbola. Then the eccentricity e of the hyperbola, satisfies

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

Q. If $PQ$ is a double ordinate of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ such that $OPQ$ is an equilateral triangle, $O$ being the centre of the hyperbola, then the eccentricity $e$ of the hyperbola satisfies

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

Q. If $PQ$ is a double ordinate of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ such that $OPQ$ is an equilateral triangle, $O$ being the centre of the hyperbola, then the eccentricity $e$ of the hyperbola satisfies

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