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