Scelta multipla
Find the equations for the asymptotes of the hyperbola .
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19. Conic Sections
Hyperbolas at the Origin
Scelta multipla
Given the hyperbola , find the length of the -axis and the -axis.
A
,
B
C
D
Guida verificata passo dopo passo1
Identify the standard form of the hyperbola equation: \( \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \). In this case, \( a^2 = 25 \) and \( b^2 = 9 \).
Calculate the value of \( a \) by taking the square root of \( a^2 \): \( a = \sqrt{25} = 5 \).
Calculate the value of \( b \) by taking the square root of \( b^2 \): \( b = \sqrt{9} = 3 \).
The length of the \( a \)-axis (transverse axis) is \( 2a \), which is \( 2 \times 5 = 10 \).
The length of the \( b \)-axis (conjugate axis) is \( 2b \), which is \( 2 \times 3 = 6 \).
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