Find the center, foci, and asymptotes of the hyperbola.
-$$x ^ { 2 } - \frac { y ^ { 2 } } { 16 } = 1$$
A) $\mathrm { C } : ( 0,0 ) ; \mathrm { F } : ( 4,0 ) , ( - 4,0 ) ; \mathrm { A } : \mathrm { y } = \frac { 1 } { 4 } \mathrm { x } , \mathrm { y } = - \frac { 1 } { 4 } \mathrm { x }$
B) C: $( 0,0 ) ; \mathrm { F } : ( \sqrt { 17 } , 0 ) , ( - \sqrt { 17 } , 0 ) ; \mathrm { A } : \mathrm { y } = 4 \mathrm { x } , \mathrm { y } = - 4 \mathrm { x }$
C) C: $( 0,0 ) ; \mathrm { F } : ( \sqrt { 17 } , 0 ) , ( - \sqrt { 17 } , 0 ) ; \mathrm { A } : \mathrm { y } = \frac { 1 } { 5 } \mathrm { x } , \mathrm { y } = - \frac { 1 } { 5 } \mathrm { x }$
D) C: $( 4,0 ) ; F : ( \sqrt { 17 } , 0 ) , ( - \sqrt { 17 } , 0 ) ; A : y = \frac { 1 } { 4 } x , y = - \frac { 1 } { 4 } x$

Question

Quizplus · Accepted Answer

The given equation is in the form of a hyperbola centered at the origin $(0,0)$, with $a^2 = 1$ and $b^2 = 16$. The foci are found using $c^2 = a^2 + b^2$, which gives $c^2 = 1 + 16 = 17$, so the foci are $(\pm\sqrt{17}, 0)$. The asymptotes for a hyperbola centered at the origin are given by $y = \pm\frac{b}{a}x$, which in this case are $y = \pm4x$, since $a = 1$ and $b = 4$.

Find the Center, Foci, and Asymptotes of the Hyperbola x2−y216=1x ^ { 2 } - \frac { y ^ { 2 } } { 16 } = 1x2−16y2​=1

Find the Center, Foci, and Asymptotes of the Hyperbola $x ^ { 2 } - \frac { y ^ { 2 } } { 16 } = 1$