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
Step 1: 4y2 - 25x2 = 100 [Equation of hyperbola.]
Step 2:y 2 / 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