Write the standard form of the equation of the hyperbola subject to the given conditions.
-Vertices: $( 3,0 ) , ( - 3,0 )$; Foci: $( 5,0 ) , ( - 5,0 )$
A) $\frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { 9 } = 1$
B) $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 25 } = 1$
C) $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 16 } = 1$
D) $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 16 } = 1$

Question

Quizplus · Accepted Answer

The vertices and foci are aligned along the x-axis, indicating the major axis is horizontal. The distance between the center and a vertex (a) is 3, so $a^2 = 9$. The distance from the center to a focus (c) is 5, so $c^2 = 25$. Using $c^2 = a^2 + b^2$, we find $b^2 = 25 - 9 = 16$. Thus, the standard form is $\frac{x^2}{9} - \frac{y^2}{16} = 1$.

Write the Standard Form of the Equation of the Hyperbola (3,0),(−3,0)( 3,0 ) , ( - 3,0 )(3,0),(−3,0)

Write the Standard Form of the Equation of the Hyperbola $( 3,0 ) , ( - 3,0 )$