Find an equation for the hyperbola described.
-center at $( 9,4 )$; focus at $( 7,4 )$; vertex at $( 8,4 )$

A) $( x - 9 ) ^ { 2 } - \frac { ( y - 4 ) ^ { 2 } } { 3 } = 1$

B) $( x - 4 ) ^ { 2 } - \frac { ( y - 9 ) ^ { 2 } } { 3 } = 1$

C) $\frac { ( x - 4 ) ^ { 2 } } { 3 } - ( y - 9 ) ^ { 2 } = 1$

D) $\frac { ( x - 9 ) ^ { 2 } } { 3 } - ( y - 4 ) ^ { 2 } = 1$

Question

Find an equation for the hyperbola described.
-center at $( 9,4 )$; focus at $( 7,4 )$; vertex at $( 8,4 )$

A) $( x - 9 ) ^ { 2 } - \frac { ( y - 4 ) ^ { 2 } } { 3 } = 1$

B) $( x - 4 ) ^ { 2 } - \frac { ( y - 9 ) ^ { 2 } } { 3 } = 1$

C) $\frac { ( x - 4 ) ^ { 2 } } { 3 } - ( y - 9 ) ^ { 2 } = 1$

D) $\frac { ( x - 9 ) ^ { 2 } } { 3 } - ( y - 4 ) ^ { 2 } = 1$

Quizplus · Accepted Answer

The center of the hyperbola is at (9,4), and since the focus and vertex are also on the same horizontal line (y=4), this indicates a horizontal hyperbola. The distance from the center to a vertex (a) is 1 (from (9,4) to (8,4)), and the distance from the center to a focus (c) is 2 (from (9,4) to (7,4)). Using the relationship $c^2 = a^2 + b^2$, we find $b^2 = 3$. Thus, the equation is $(x - 9)^2 - \frac{(y - 4)^2}{3} = 1$.

Find an Equation for the Hyperbola Described (9,4)( 9,4 )(9,4) ; Focus At

Find an Equation for the Hyperbola Described $( 9,4 )$ ; Focus At