Processing math: 100%

Conjugate Hyperbola

What is conjugate hyperbola?

If the transverse axis and conjugate axis of any hyperbola be respectively the conjugate axis and transverse axis of another hyperbola then the hyperbolas are called the conjugate hyperbola to each other.

The conjugate hyperbola of the hyperbola x2a2 - y2b2 = 1 is - x2a2 + y2b2 = 1

The transverse axes of the hyperbola x2a2 - y2b2 = 1 is along x-axis and its length = 2a.

The conjugate axes of the hyperbola x2a2 - y2b2 = 1 is along y-axis and its length = 2b.

Therefore, the hyperbola conjugate to x2a2 - y2b2 = 1 will have its transverse and conjugate axes along y and x-axes respectively while the length of transverse and conjugate axes will be 2b and 2a respective.

Therefore, the equation of the hyperbola conjugate to x2a2 - y2b2 = 1 is - x2a2 + y2b2 = 1

Thus, the hyperbolas x2a2 - y2b2 = 1 and - x2a2 + y2b2 = 1 are conjugate to each other.

The eccentricity of the conjugate hyperbola is given by a2 = b2(e2 - 1).


Now we will come across various results related to the hyperbola x2a2 - y2b2 = 1 ……………. (i) and its conjugate - x2a2 + y2b2 = 1 ………………. (ii).

1. The co-ordinates of the centre of both the hyperbola (i) and its conjugate hyperbola (ii) are (0, 0).

2. The co-ordinates of the vertices of the hyperbola (i) are (-a, 0) and (a, 0) and its conjugate hyperbola (ii) are (0, -b) and (0, b).

3. The co-ordinates of the foci of the hyperbola (i) are (-ae, 0) and (ae, 0) and its conjugate hyperbola (ii) are (0, be) and (0, -be).

4. The length of the transverse axis of the hyperbola (i) is 2a and its conjugate hyperbola (ii) is 2b.

5. The length of the conjugate axis of the hyperbola (i) is 2b and its conjugate hyperbola (ii) is 2a.

6. The eccentricity of the hyperbola (i) is e = a2+b2a2 or, b2 = a2(e2 - 1) and its conjugate hyperbola (ii) is e = b2+a2b2 or, a2 = b2(e2 - 1).

7. The length of the latusrectum of the hyperbola (i) is 2b2a and its conjugate hyperbola (ii) is 2a2b.

8. The equation of the transverse axis of the hyperbola (i) is y = 0 and its conjugate hyperbola (ii) is x = 0.

9. The equation of the conjugate axis of the hyperbola (i) is x = 0 and its conjugate hyperbola (ii) is y = 0.

The Hyperbola






11 and 12 Grade Math

From Conjugate Hyperbola to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.




Share this page: What’s this?

Recent Articles

  1. Worksheet on Area of a Square and Rectangle | Area of Squares & Rectan

    Jul 19, 25 05:00 AM

    Area and Perimeter of Square and Rectangle
    We will practice the questions given in the worksheet on area of a square and rectangle. We know the amount of surface that a plane figure covers is called its area. 1. Find the area of the square len…

    Read More

  2. Area of Rectangle Square and Triangle | Formulas| Area of Plane Shapes

    Jul 18, 25 10:38 AM

    Area of a Square of Side 1 cm
    Area of a closed plane figure is the amount of surface enclosed within its boundary. Look at the given figures. The shaded region of each figure denotes its area. The standard unit, generally used for…

    Read More

  3. What is Area in Maths? | Units to find Area | Conversion Table of Area

    Jul 17, 25 01:06 AM

    Concept of Area
    The amount of surface that a plane figure covers is called its area. It’s unit is square centimeters or square meters etc. A rectangle, a square, a triangle and a circle are all examples of closed pla…

    Read More

  4. Worksheet on Perimeter | Perimeter of Squares and Rectangle | Answers

    Jul 17, 25 12:40 AM

    Most and Least Perimeter
    Practice the questions given in the worksheet on perimeter. The questions are based on finding the perimeter of the triangle, perimeter of the square, perimeter of rectangle and word problems. I. Find…

    Read More

  5. Formation of Square and Rectangle | Construction of Square & Rectangle

    Jul 16, 25 11:46 PM

    Construction of a Square
    In formation of square and rectangle we will learn how to construct square and rectangle. Construction of a Square: We follow the method given below. Step I: We draw a line segment AB of the required…

    Read More