# RS Aggarwal Class 11 Chapter 24 Solutions (Hyperbola)

RS Aggarwal Class 11 Solutions for Chapter 24 will help you solve all the questions related to the Chapter. It clears the concepts and increases your speed and accuracy during CBSE exam. The methods used in RS Aggarwal Solutions are extremely easy and can be used by students as they are designed according to the latest syllabus and exam pattern.

The Chapter consists of 1 exercise which has 23 questions in it. Along with the exercise, there are many solved examples in the Chapter in which students can practice well. The benefit that RS Aggarwal Class 11 Solutions for Chapter 24 gives is that with the answers of all the questions are given in detail and therefore you can just go through the solutions and grasp the concepts in no time.

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## Important Points of the Chapter: Hyperbola

- In a plain when there is a locus of a point, which moves inside the plane in a way that the ratio of its distance from a point which is fixed in the same plane to its distance from a given fixed line always stays constant, this result is always greater than the unity and this phenomenon is known as Hyperbola.
- The point which is fixed is called the focus.
- The line which is fixed is the directrix
- The ratio found is called the eccentricity.
- Both the foci lie on the x-axis and centre O lies at the origin.
- The line segments perpendicular to the transverse axis through any of the foci such that their endpoints lie on the hyperbola are defined as the latus rectum of a hyperbola
- The length of the latus rectum is 2b²/a.
- The difference of the focal distance of any point on a hyperbola is constant
- The distance of a point on the hyperbola from the focus is called its the focal distance
- Points on the hyperbola, the normals at which passes through a given point are called co-normal points
- The sum of the eccentric angles of co-normal points is an odd ion multiple of π.
- Two points are known as conjugate points in respect to a hyperbola when each of the points lies on the polar of the other point.
- When a line from 2 lines along the hyperbola passes through the pole of another line, then the 2 lines are called Conjugate lines.
- Two lines are called conjugate lines along with a hyperbola when anyone line passes through the pole of another line.
- When every diameter of a hyperbola bisects the chords parallel to each other then diameters are known as Conjugate Diameter.
- In a hyperbola, when there is a pair of conjugate diameters only 1 meets the hyperbola in actual point.
- The orthocentre of the triangle inscribed in a rectangular hyperbola lies on the hyperbola.

## Topics Covered in RS Aggarwal Solutions Chapter 24 Hyperbola

The following different topics are covered under this Chapter:

- Transverse and conjugate axes
- Equation of hyperbola in a different form
- Conjugate hyperbola
- Equation of tangent hyperbola
- The focal distance of a point
- Equation of chord
- Diameter and conjugate diameter
- Co-normal points
- Conjugate points and conjugate lines
- Rectangular hyperbola
- Rectangular hyperbola of the form xy = c²
- Normal equation of rectangular hyperbola xy = c²
- Tangent equation of rectangular hyperbola xy = c²

**Important Formulas for Solving the Questions**

**Horizontal Hyperbola**

For the general form of a hyperbola

x²/a² – y²/b² = 1

**Length of Transverse Axis: **2a

**Length of Conjugate Axis: **2b

**Vertices: **(±a ,0)

**Foci: **(±c, 0)

**Eccentricity: **e = c/a

**Latus Rectum: **2b²/a

**Vertical Hyperbola**

** **For the general form of a hyperbola

y²/a² – x²/b² = 1

**Length of Transverse Axis: **2a

**Length of Conjugate Axis: **2b

**Vertices: **( 0, ±a )

**Foci: **( 0, ±c)

**Eccentricity: **e = c/a

**Latus Rectum: **2b²/a

## Exercise Wise Discussion of RS Aggarwal Class 11 Chapter 24 Hyperbola

This exercise 23 has 23 questions in which you have to:

- Find the length of axes for the given Hyperbola
- Find the coordinates of the vertices for the given Hyperbola
- Find the coordinates of the foci for the given Hyperbola
- Find the eccentricity for the given Hyperbola
- Find the length of the latus rectum for the given Hyperbola
- Find the equation of the Hyperbola when vertices and foci are given

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