Write Equations of Hyperbolas in Standard Form
-Center: $( 6,1 )$; Focus: $( - 1,1 )$; Vertex: $( 5,1 )$
A) $( x - 6 ) ^ { 2 } - \frac { ( y - 1 ) ^ { 2 } } { 48 } = 1$
B) $\frac { ( x - 6 ) ^ { 2 } } { 48 } - ( y - 1 ) ^ { 2 } = 1$
C) $( x - 1 ) ^ { 2 } - \frac { ( y - 6 ) ^ { 2 } } { 48 } = 1$
D) $\frac { ( x - 1 ) ^ { 2 } } { 48 } - ( y - 6 ) ^ { 2 } = 1$

Question

Quizplus · Accepted Answer

The standard form of a hyperbola with a horizontal transverse axis is $\frac{(x-h)^2}{a^2} - \frac{(y-k)^2}{b^2} = 1$, where $(h, k)$ is the center. The distance between the center and a focus (c) is 7 units (from $(6,1)$ to $(-1,1)$), and the distance between the center and a vertex (a) is 1 unit (from $(6,1)$ to $(5,1)$). Using $c^2 = a^2 + b^2$, we find $b^2 = 48$. Thus, the correct equation is $(x - 6)^2 - \frac{(y - 1)^2}{48} = 1$.

Write Equations of Hyperbolas in Standard Form -Center (6,1)( 6,1 )(6,1)

Write Equations of Hyperbolas in Standard Form
-Center $( 6,1 )$