TRANSVERSE AXIS

Transverse Axis

Definition Of Transverse Axis

The segment of length 2a whose endpoints are the vertices of a hyperbola. (same definition)

Video Examples: Find Equation Gvien Focus, Transverse Axis Length

Solved Example on Transverse Axis

Ques: Find the length of transverse axis of the hyperbola 4y² - 25x² = 100.

Choices:

A. y = 0
B. y = 5
C. x = 0
D. x = 2
Correct Answer: D

Solution:

Step 1: 4y² - 25x² = 100 [Equation of hyperbola.]
Step 2:y²/25 - x² / 4 = 1 [Divide both sides by 100.]
Step 3: This is in the standard form y² / b ² - x² /a = 1 of a hyperbola whose transverse axis is y - axis,
where a² = 4 and b² = 25.
Step 4: a = 2 and b = 5 [Solve for a, b.]
Step 5: So, the length of the transverse axis of the hyperbola is 2a = 2(2) = 4

Quick Summary

The transverse axis connects the vertices of a hyperbola.
Its length is equal to 2a, where 'a' is a parameter in the hyperbola's equation.

\[ 2a \]

🍎 Teacher Insights

Emphasize the visual representation of the transverse axis on the hyperbola graph. Use examples with different orientations of the hyperbola.

🎓 Prerequisites

Algebra
Coordinate Geometry
Hyperbola Basics

Check Your Knowledge

Q1: What is the length of the transverse axis of the hyperbola 4y^2 - 25x^2 = 100?

y = 0 y = 5 x = 0 x = 2

Frequently Asked Questions

Q: What is the difference between the transverse and conjugate axis?
A: The transverse axis passes through the vertices, while the conjugate axis is perpendicular to it and passes through the center of the hyperbola.

Q: How do I find the length of the transverse axis?
A: The length is 2a, where 'a' is found in the equation of the hyperbola (x^2/a^2 - y^2/b^2 = 1 or y^2/a^2 - x^2/b^2 = 1).