Find the equation of the hyperbola with center $( 1,3 ) , a = 2$ and $b = 4$. Transverse axis is horizontal.
A)
$$\frac { ( x - 1 ) ^ { 2 } } { 4 } - \frac { ( y - 3 ) ^ { 2 } } { 16 } = 1$$
B)
$$\frac { ( x - 2 ) ^ { 2 } } { 2 } - \frac { ( y - 3 ) ^ { 2 } } { 16 } = 1$$
C)
$$\frac { ( x + 1 ) ^ { 2 } } { 4 } - \frac { ( y + 3 ) ^ { 2 } } { 16 } = 1$$
D)
$$\frac { ( x - 1 ) ^ { 2 } } { 4 } + \frac { ( y - 3 ) ^ { 2 } } { 16 } = 1$$

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 x-axis, and $b$ is the distance from the center to the vertices along the y-axis. Given the center $(1,3)$, $a=2$, and $b=4$, substituting these values into the formula gives $\frac{(x-1)^2}{2^2} - \frac{(y-3)^2}{4^2} = 1$, which simplifies to $\frac{(x-1)^2}{4} - \frac{(y-3)^2}{16} = 1$.

Find the Equation of the Hyperbola with Center (1,3),a=2( 1,3 ) , a = 2(1,3),a=2

Find the Equation of the Hyperbola with Center $( 1,3 ) , a = 2$