Find the equation of the hyperbola with vertices (2, 0), (-2, 0) and focus (4, 0).
A) $\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 12 } = 1$
B) $\frac { y ^ { 2 } } { 4 } - \frac { x ^ { 2 } } { 12 } = 1$
C) $\frac { x ^ { 2 } } { 12 } - \frac { y ^ { 2 } } { 4 } = 1$
D) $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 12 } = 1$
E)none of these

Question

Find the equation of the hyperbola with vertices (2, 0), (-2, 0) and focus (4, 0). 
A) $\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 12 } = 1$
B) $\frac { y ^ { 2 } } { 4 } - \frac { x ^ { 2 } } { 12 } = 1$
C) $\frac { x ^ { 2 } } { 12 } - \frac { y ^ { 2 } } { 4 } = 1$
D) $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 12 } = 1$
E)none of these

Quizplus · Accepted Answer

The vertices at (2, 0) and (-2, 0) indicate that the hyperbola is centered at the origin and opens along the x-axis. The distance between the center and either vertex is 2, so $a = 2$, and $a^2 = 4$. The focus at (4, 0) means $c = 4$, and $c^2 = 16$. For a hyperbola, $c^2 = a^2 + b^2$, so $16 = 4 + b^2$, leading to $b^2 = 12$. Thus, the equation is $\frac{x^2}{4} - \frac{y^2}{12} = 1$.

Find the Equation of the Hyperbola with Vertices (2, 0) x24−y212=1\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 12 } = 14x2​−12y2​=1

Find the Equation of the Hyperbola with Vertices (2, 0) $\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 12 } = 1$