Find the vertices and locate the foci for the hyperbola whose equation is given.
-$$y = \pm \sqrt { x ^ { 2 } - 6 }$$
A) vertices: $( - \sqrt { 6 } , 0 ) , ( \sqrt { 6 } , 0 )$
foci: $( - 2 \sqrt { 3 } , 0 ) , ( 2 \sqrt { 3 } , 0 )$
B) vertices: $( - 6,0 ) , ( 6,0 )$
foci: $( - \sqrt { 6 } , 0 ) , ( \sqrt { 6 } , 0 )$
C) vertices: $( - 6,0 ) , ( 6,0 )$
foci: $( - 2 \sqrt { 3 } , 0 ) , ( 2 \sqrt { 3 } , 0 )$
D) vertices: $( 0 , - \sqrt { 6 } ) , ( 0 , \sqrt { 6 } )$
foci: $( 0 , - 2 \sqrt { 3 } ) , ( 0,2 \sqrt { 3 } )$

Question

Quizplus · Accepted Answer

By comparing the given equation with the standard form $y^2/a^2 - x^2/b^2 = 1$, we see that $a=1$ and $b=\sqrt{6}$. Therefore, the vertices are $(0,\pm a) = (0,\pm 1)$ and the foci are $(0,\pm c)$ where $c=\sqrt{a^2+b^2} = \sqrt{7}$. Using these values, we obtain the coordinates of the vertices and foci given in choice A.

Find the Vertices and Locate the Foci for the Hyperbola y=±x2−6y = \pm \sqrt { x ^ { 2 } - 6 }y=±x2−6​

Find the Vertices and Locate the Foci for the Hyperbola $y = \pm \sqrt { x ^ { 2 } - 6 }$