Write the standard form of the equation of the hyperbola centered at the origin. Vertices: $( 0 , - 2 ) , ( 0,2 )$ Asymptotes: $y = 4 x , y = - 4 x$
A) $\frac { y ^ { 2 } } { 4 } - \frac { x ^ { 2 } } { 1 / 4 } = 1$
B) $\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 64 } = 1$
C) $\frac { y ^ { 2 } } { 4 } - \frac { x ^ { 2 } } { 64 } = 1$
D) $\frac { x ^ { 2 } } { 64 } - \frac { y ^ { 2 } } { 4 } = 1$
E) $\frac { y ^ { 2 } } { 1 / 4 } - \frac { x ^ { 2 } } { 4 } = 1$

Question

Quizplus · Accepted Answer

The vertices are on the y-axis, so the transverse axis is vertical. The distance between the vertices is 4, so $2a = 4$ and $a = 2$. The asymptotes have slopes of 4 and -4, so $b = 4$. The standard form of the equation is $\frac{y^2}{a^2} - \frac{x^2}{b^2} = 1$, so the equation is $\frac{y^2}{4} - \frac{x^2}{16} = 1$.

Write the Standard Form of the Equation of the Hyperbola (0,−2),(0,2)( 0 , - 2 ) , ( 0,2 )(0,−2),(0,2)

Write the Standard Form of the Equation of the Hyperbola $( 0 , - 2 ) , ( 0,2 )$