Write Equations of Hyperbolas in Standard Form
-Endpoints of transverse axis: $( - 5,0 ) , ( 5,0 )$; foci: $( - 11,0 ) , ( - 11,0 )$
A) $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 96 } = 1$
B) $\frac { x ^ { 2 } } { 96 } - \frac { y ^ { 2 } } { 25 } = 1$
C) $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 121 } = 1$
D) $\frac { x ^ { 2 } } { 121 } - \frac { y ^ { 2 } } { 25 } = 1$

Question

Quizplus · Accepted Answer

The standard form of a horizontal hyperbola is $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$, where $2a$ is the length of the transverse axis and $c$ is the distance from the center to a focus. Here, $2a = 10$ (from $-5$ to $5$), so $a^2 = 25$. The distance from the center to a focus is $c = 11$, so $c^2 = 121$. Using $c^2 = a^2 + b^2$, we find $b^2 = 121 - 25 = 96$. Thus, the equation is $\frac{x^2}{25} - \frac{y^2}{96} = 1$.

Write Equations of Hyperbolas in Standard Form -Endpoints of Transverse (−5,0),(5,0)( - 5,0 ) , ( 5,0 )(−5,0),(5,0)

Write Equations of Hyperbolas in Standard Form
-Endpoints of Transverse $( - 5,0 ) , ( 5,0 )$