Question

use vertices and asymptotes to graph the hyperbola. locate the foci and find the equations of the asymptotes.\\(\frac{x^2}{49} - \frac{y^2}{100} = 1\\)\
graph the hyperbola. choose the correct graph below.\
the foci is/are at the point(s) \\(\square\\).\
(type an ordered pair. type an exact answer, using radicals as needed. use a comma to separate answers as needed.)

Explanation:

Step1: Identify hyperbola type

Standard form: $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ (horizontal transverse axis). Here $a^2=49\Rightarrow a=7$, $b^2=100\Rightarrow b=10$.

Step2: Find vertices

Vertices at $(\pm a,0)=(\pm7,0)$, so graph opens left/right.

Step3: Calculate foci

$c^2=a^2+b^2=49+100=149\Rightarrow c=\sqrt{149}$. Foci at $(\pm\sqrt{149},0)$.

Step4: Match graph

Graph A has horizontal opening, vertices near $(\pm7,0)$—matches.

Answer:

Correct graph: A
Foci: $(-\sqrt{149}, 0), (\sqrt{149}, 0)$