Find the equation of the hyperbola with center $( 3,1 ) , a = 5$ and $b = 4$. Transverse axis is horizontal.
A) $\frac { ( x - 3 ) ^ { 2 } } { 25 } - \frac { ( y - 1 ) ^ { 2 } } { 16 } = 1$
B) $\quad \frac { ( x - 3 ) ^ { 2 } } { 25 } + \frac { ( y - 1 ) ^ { 2 } } { 16 } = 1$
C) $\quad \frac { ( x - 4 ) ^ { 2 } } { 23 } - \frac { ( y - 1 ) ^ { 2 } } { 16 } = 1$
D) $\quad \frac { ( x + 3 ) ^ { 2 } } { 25 } - \frac { ( y + 1 ) ^ { 2 } } { 16 } = 1$
E) none of these

Question

Quizplus · Accepted Answer

The equation of a hyperbola with a horizontal transverse axis is given by $\frac{(x-h)^2}{a^2} - \frac{(y-k)^2}{b^2} = 1$, where $(h,k)$ is the center, $a$ is the distance from the center to the vertices along the transverse axis, and $b$ is the distance from the center to the vertices along the conjugate axis. Given the center $(3,1)$, $a=5$, and $b=4$, the equation becomes $\frac{(x-3)^2}{25} - \frac{(y-1)^2}{16} = 1$.

Find the Equation of the Hyperbola with Center (3,1),a=5( 3,1 ) , a = 5(3,1),a=5

Find the Equation of the Hyperbola with Center $( 3,1 ) , a = 5$