Find the center, foci, and asymptotes of the hyperbola.
-$$x ^ { 2 } - \frac { y ^ { 2 } } { 25 } = 1$$
A) C: $( 0,0 ) ; F : ( 5,0 ) , ( - 5,0 ) ; A : y = \frac { 1 } { 5 } x , y = - \frac { 1 } { 5 } x$
B) C: $( 0,0 ) ; F : ( \sqrt { 26 } , 0 ) , ( - \sqrt { 26 } , 0 ) ; A : y = 5 x , y = - 5 x$
C) C: $( 0,0 ) ; F : ( \sqrt { 26 } , 0 ) , ( - \sqrt { 26 } , 0 ) ; A : y = \frac { 1 } { 6 } x , y = - \frac { 1 } { 6 } x$
D) C: $( 5,0 ) ; F : ( \sqrt { 26 } , 0 ) , ( - \sqrt { 26 } , 0 ) ; A : y = \frac { 1 } { 5 } x , y = - \frac { 1 } { 5 } x$

Question

Quizplus · Accepted Answer

The given equation is in the form $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$, with $a^2 = 1$ and $b^2 = 25$, indicating a hyperbola centered at (0,0). The distance from the center to the foci is $\sqrt{a^2 + b^2} = \sqrt{1 + 25} = \sqrt{26}$, so the foci are $(\sqrt{26}, 0)$ and $(- \sqrt{26}, 0)$. The asymptotes for a hyperbola of this form are $y = \pm \frac{b}{a}x$, which simplifies to $y = \pm 5x$, given $b^2 = 25$ and $a^2 = 1$.

Find the Center, Foci, and Asymptotes of the Hyperbola x2−y225=1x ^ { 2 } - \frac { y ^ { 2 } } { 25 } = 1x2−25y2​=1

Find the Center, Foci, and Asymptotes of the Hyperbola $x ^ { 2 } - \frac { y ^ { 2 } } { 25 } = 1$