Find the foci of the hyperbola.
-$4 x ^ { 2 } - y ^ { 2 } = 4$
A) $( \sqrt { 5 } , 0 ) , ( - \sqrt { 5 } , 0 )$
B) $( 2,0 ) , ( - 2,0 )$
C) $( 0 , \sqrt { 5 } ) , ( 0 , - \sqrt { 5 } )$
D) $( 0,2 ) , ( 0 , - 2 )$

Question

Quizplus · Accepted Answer

The equation of the hyperbola is given in the form $4x^2 - y^2 = 4$, which can be rewritten as $\frac{x^2}{1} - \frac{y^2}{4} = 1$. This indicates a hyperbola centered at the origin with a horizontal transverse axis. The distance of the foci from the center along the x-axis is given by $c = \sqrt{a^2 + b^2}$, where $a^2 = 1$ and $b^2 = 4$. Thus, $c = \sqrt{1 + 4} = \sqrt{5}$, and the foci are at $(\sqrt{5}, 0)$ and $(- \sqrt{5}, 0)$.

Find the Foci of the Hyperbola 4x2−y2=44 x ^ { 2 } - y ^ { 2 } = 44x2−y2=4

Find the Foci of the Hyperbola $4 x ^ { 2 } - y ^ { 2 } = 4$