Join thousands of students who trust us to help them ace their exams!Watch the first video
Multiple Choice
Given the hyperbola , find the length of the -axis and the -axis.
A
B
C
D
Verified step by step guidance
1
Identify the standard form of the hyperbola equation: \( \frac{y^2}{a^2} - \frac{x^2}{b^2} = 1 \). This indicates a vertical hyperbola because the \( y^2 \) term is positive.
Compare the given equation \( \frac{y^2}{100} - \frac{x^2}{139} = 1 \) with the standard form to determine \( a^2 = 100 \) and \( b^2 = 139 \).
Calculate \( a \) by taking the square root of \( a^2 \): \( a = \sqrt{100} = 10 \).
Calculate \( b \) by taking the square root of \( b^2 \): \( b = \sqrt{139} \).
The length of the transverse axis (a-axis) is \( 2a = 2 \times 10 = 20 \) and the length of the conjugate axis (b-axis) is \( 2b = 2 \times \sqrt{139} \).