Conjugate Axis of Hyperbola

Q.

A certain orbital has no angular nodes and two radial nodes. The orbital is:

1. $2\mathrm{p}$

2. $3\mathrm{p}$

3. $2\mathrm{s}$

4. $3\mathrm{s}$

Q.

Consider the letters of English alphabets, $\text{A to Z}$. List among them the letters which have vertical lines of symmetry (like $\text{A}$).

Q.

What the eccentricity of the hyperbola with its principal axes along the

coordinate axes and which passes through (3, 0) and $(3\sqrt{2},2)$

1. 

2. 

3. 

4. 

Q. The length of the conjugate axis of the hyperbola $9x^2-90x-25y^2+150y-225=0$ is units

Q.

In a hyperbola e=2 and the length of semitransverse axis is 3 and the length of conjugate axis is

1. $3\sqrt{3}$

2. $6\sqrt{3}$

3. $6\sqrt{2}$

4. $3\sqrt{2}$

Q.

Give for parabola $y^2=4ax$, One of the tangents from the point (l, m)

touch the parabola at $(a{t_1}^2,2a{t_1}^2).$ The other point of contact in

terms of $a,t_1,l,m$ is $(\frac{l^2}{a{t_1}^2},\frac{2l}{t_1})$.

1. True

2. False

Q.

What the eccentricity of the hyperbola with its principal axes along the

coordinate axes and which passes through (3, 0) and $(3\sqrt{2},2)$

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

2. $\frac{\sqrt{13}}{3}$

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

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

Q.

Select the right options about a hyperbola.

1. Conjugate axis is the axis of the hyperbola that passes through the foci

2. A transverse axis always pass through the origin

3. The straight line through the centre which is perpendicular to the transverse axis doesn't meet hyperbola in real point.

4. Eccentricity is the ratio of 2 distances

Q. The circle $x^2+y^2–8x=0$ and hyperbola $\frac{x^2}{9}-\frac{y^2}{4}=1$ intersect at the points $A$ and $B$.

1. Option c
2. Option d
3. Option b
4. Option a

Q. The axis of symmetry of a parabola is $x=6$, and one point on the parabola is $(2,8)$. What is another point on the parabola?

Q.

In a hyperbola e=2 and the length of semitransverse axis is 3 and the length of conjugate axis is

1. 

2. 

3. 

4. 

Q. Find the angles made by the following vectors with the coordinate axes:
(i) $(\hat{i}-\hat{j}+\hat{k})$ (ii) $(\hat{j}-\hat{k})$ (iii) $(\hat{i}-4\hat{j}+5\hat{k})$