Find the equation of the hyperbola with center $( 2,1 ) , a = 5$ and $b = 2$. Transverse axis is horizontal.
A) $\quad \frac { ( x - 3 ) ^ { 2 } } { 23 } - \frac { ( y - 1 ) ^ { 2 } } { 4 } = 1$
B) $\quad \frac { ( x - 2 ) ^ { 2 } } { 25 } - \frac { ( y - 1 ) ^ { 2 } } { 4 } = 1$
C) $\quad \frac { ( x + 2 ) ^ { 2 } } { 25 } - \frac { ( y + 1 ) ^ { 2 } } { 4 } = 1$
D) $\quad \frac { ( x - 2 ) ^ { 2 } } { 25 } + \frac { ( y - 1 ) ^ { 2 } } { 4 } = 1$
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 $(2,1)$, $a=5$, and $b=2$, the equation becomes $\frac{(x-2)^2}{25} - \frac{(y-1)^2}{4} = 1$.

Find the Equation of the Hyperbola with Center (2,1),a=5( 2,1 ) , a = 5(2,1),a=5

Find the Equation of the Hyperbola with Center $( 2,1 ) , a = 5$