Transverse Axis of Hyperbola

Q.

What is the eccentricity of a rectangular hyperbola?

1. $\sqrt{2}$

2. $\sqrt{3}$

3. $\sqrt{5}$

4. $\sqrt{6}$

Q. The eccentricity of the hyperbola whose length of conjugate axis is equal to half of the distance between its foci is $e$, then $3e^2=$

Q. The equation of hyperbola with vertices at $(0,\pm 6)$ and $e=\frac{5}{3}$
(where $e$ is eccentricity)

1. $\frac{y^2}{36}-\frac{x^2}{64}=1$

2. $\frac{x^2}{64}-\frac{y^2}{36}=1$
3. $\frac{x^2}{36}-\frac{y^2}{64}=1$
4. $\frac{y^2}{35}-\frac{x^2}{25}=1$

Q.

A standard hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ of eccentricity 'e' is given as below.

Choose the correct options.[S is the focus and dotted line is a directrix.]

1. \)

2. AB=2a

3. QS=me

4. SB=a(e-1)

Q. Let $A,B$ be two distinct points on the parabola $y^2=4x$. If the axis of the parabola touches a circle of radius $r$ having $AB$ as diameter, the slope of the line $AB$ is

1. $-\frac{1}{r}$
2. $\frac{1}{r}$
3. $\frac{2}{r}$
4. $-\frac{2}{r}$

Q. The length of conjugate axis of a hyperbola is greater than the length of transverse axis. Then the eccentricity $e$ is ,

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

Q.

The length of the transverse axis of the hyperbola $9x^2-16y^2-18x-32y-151=0is$

1. 8

2. 4

3. 2

4. 6

Q.

The transverse axis of a hyperbola is double the conjugate axes. Whats the eccentricity of the hyperbola

1. 

2. 

3. 

4. 

Q. If a chord of the ellipse $\frac{x^2}{4}+\frac{y^2}{9}=1$ touches the hyperbola $\frac{x^2}{4}-\frac{y^2}{9}=1$, and the locus of middle point of such chord is given by ${(\frac{x^2}{4}+\frac{y^2}{9})}^{{\lambda }_2}={\lambda }_1(\frac{x^2}{4}-\frac{y^2}{9})$ then ${\lambda }_1+{\lambda }_2$ is $({\lambda }_1,{\lambda }_2\in N)$

1. $4$
2. $2$
3. $1$
4. $3$

Q. Find the eccentricity of the hyperbola, the length of whose conjugate axis is $\frac{3}{4}$ of the length of transverse axis.

Q.

What is meant by the eccentricity of a hyperbola?

Q. A hyperbola has its centre at the origin, passes through the point $(4,2)$ and has transverse axis of length $4$ along the $x$-axis. Then the eccentricity of the hyperbola is :

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

Q. A hyperbola has its centre at the origin, passes through the point $(4,2)$ and has transverse axis of length $4$ along the $x$-axis. Then the eccentricity of the hyperbola is :

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

Q.

If the lengths of transverse and conjugate axis of the hypberbola are 4, 2 then the distance Between the foci is

1. 

2. 

3. 

4. 

Q. If $P(-3,2)$ is one end of the focal chord $PQ$ of the parabola $y^2+4x+4y=0$, then the slope of the $PQ$ is

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

Q. If a parabola whose length of latus rectum is 4a touches both the coordinate axes then the focus of its locus is

1. $xy=a^2(x^2+y^2)$
2. $x^2{y}^2=a^2(x^2+y^2)$
3. $x^2-y^2=a^2(x^2+y^2)$
4. $x^2{y}^2=a^2(x^2-y^2)$

Q. The line $lx+my+n=0$ is normal to the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$; then $n^2(\frac{a^2}{l^2}-\frac{b^2}{m^2})$ is equal to

1. $a^2-b^2$
2. $(a^2-b^2{)}^2$
3. $(a^2+b^2)$
4. $(a^2+b^2{)}^2$

Q.

In a given standrard hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$.What is the length of transverse axis?

1. a

2. b

3. 2a

4. 2b

Q. The length of the latus rectum of the curve traced by the point $(\frac{3}{2}[t+\frac{1}{t}],\frac{\sqrt{7}}{2}[t-\frac{1}{t}])$, where $t(\ne 0)$ is a parameter, is equal to

1. $\frac{6}{7}$
2. $\frac{14}{3}$
3. $\frac{7}{3}$
4. $\frac{3}{7}$

Q. The area of triangle formed by tangent to the hyperbola $2xy=a^2$ and coordinates axes is -

1. $a^2$
2. $\frac{a^2}{2}$
3. $2a^2$
4. $\frac{3a^2}{2}$

Q. The equation of hyperbola with vertices at $(0,\pm 6)$ and $e=\frac{5}{3}$
(where $e$ is eccentricity)

1. $\frac{y^2}{36}-\frac{x^2}{64}=1$

2. $\frac{x^2}{64}-\frac{y^2}{36}=1$
3. $\frac{x^2}{36}-\frac{y^2}{64}=1$
4. $\frac{y^2}{35}-\frac{x^2}{25}=1$

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

Q. If the two parabolas $y^2=4a(x-k_1)$ and $x^2=4a(y-k_2)$ always touch each other, $k_1$ and $k_2$ being variable parameters, then their point of contact lies on the curve :

1. $xy=a^2$
2. $xy=3a^2$
3. $xy=2a^2$
4. $xy=4a^2$

Q. At what point on the parabola $y^2=4x$ the normal makes equal angles with axes?

1. $(4,4)$
2. $(9,6)$
3. $(4,-4)$
4. $(1,\pm 2)$

Q. The eccentricity of the hyperbola whose length of conjugate axis is equal to half of the distance between its foci is $e$, then $3e^2=$

Q. For hyperbola $-\frac{x^2}{9}+\frac{y^2}{16}=1$, focus is is on

1. none
2. x-axis
3. y-axis
4. z-axis