Write Equations of Hyperbolas in Standard Form
-Foci: $( - 9,0 ) , ( 9,0 )$; vertices: $( - 5,0 ) , ( 5,0 )$
A) $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 56 } = 1$
B) $\frac { y ^ { 2 } } { 25 } - \frac { x ^ { 2 } } { 56 } = 1$
C) $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 81 } = 1$
D) $\frac { y ^ { 2 } } { 25 } - \frac { x ^ { 2 } } { 81 } = 1$

Question

Quizplus · Accepted Answer

The standard form of a hyperbola with a horizontal transverse axis is $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$, where $2a$ is the distance between the vertices, and $2c$ is the distance between the foci. Here, $2a = 10$ (from $-5$ to $5$), so $a^2 = 25$. The distance between the foci is $2c = 18$ (from $-9$ to $9$), so $c^2 = 81$. Using $c^2 = a^2 + b^2$, we find $b^2 = 81 - 25 = 56$. Thus, the correct equation is $\frac{x^2}{25} - \frac{y^2}{56} = 1$.

Write Equations of Hyperbolas in Standard Form -Foci (−9,0),(9,0)( - 9,0 ) , ( 9,0 )(−9,0),(9,0)

Write Equations of Hyperbolas in Standard Form
-Foci $( - 9,0 ) , ( 9,0 )$