Solve the problem.
-Find the vertices and foci of the following hyperbola:
$\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 91 } = 1$
A) Vertices: (0, 3), (0, -3); Foci: (0, 10), (0, -10)
B) Vertices: (3, 0), (-3, 0); Foci: (10, 0), (-10, 0)
C) Vertices: (0, 10), (0, -10); Foci: (0, 3), (0, -3)
D) Vertices: (9, 0), (-9, 0); Foci: (10, 0), (-10, 0)

Question

Quizplus · Accepted Answer

The given equation is of the form $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$, indicating a hyperbola centered at the origin with its transverse axis along the x-axis. The vertices are at $(\pm a, 0)$, where $a^2 = 9$, so $a = 3$, giving vertices at $(3, 0)$ and $(-3, 0)$. The foci are at $(\pm c, 0)$, where $c^2 = a^2 + b^2$. Here, $b^2 = 91$, so $c^2 = 9 + 91 = 100$, meaning $c = 10$, giving foci at $(10, 0)$ and $(-10, 0)$.

Solve the Problem x29−y291=1\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 91 } = 19x2​−91y2​=1

Solve the Problem $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 91 } = 1$