The Hyperbola
1 Locate a Hyperbola's Vertices and Foci
-$$y = \pm \sqrt { x ^ { 2 } - 10 }$$
A) vertices: $( - \sqrt { 10 } , 0 ) , ( \sqrt { 10 } , 0 )$
foci: $( - 2 \sqrt { 5 } , 0 ) , ( 2 \sqrt { 5 } , 0 )$
B) vertices: $( - 10,0 ) , ( 10,0 )$
foci: $( - \sqrt { 10 } , 0 ) , ( \sqrt { 10 } , 0 )$
C) vertices: $( - 10,0 ) , ( 10,0 )$
foci: $( - 2 \sqrt { 5 } , 0 ) , ( 2 \sqrt { 5 } , 0 )$

D) vertices: $( 0 , - \sqrt { 10 } ) , ( 0 , \sqrt { 10 } )$

foci: $( 0 , - 2 \sqrt { 5 } ) , ( 0,2 \sqrt { 5 } )$

Question

The Hyperbola
1 Locate a Hyperbola's Vertices and Foci
-$$y = \pm \sqrt { x ^ { 2 } - 10 }$$
A) vertices: $( - \sqrt { 10 } , 0 ) , ( \sqrt { 10 } , 0 )$
foci: $( - 2 \sqrt { 5 } , 0 ) , ( 2 \sqrt { 5 } , 0 )$
B) vertices: $( - 10,0 ) , ( 10,0 )$
foci: $( - \sqrt { 10 } , 0 ) , ( \sqrt { 10 } , 0 )$
C) vertices: $( - 10,0 ) , ( 10,0 )$
foci: $( - 2 \sqrt { 5 } , 0 ) , ( 2 \sqrt { 5 } , 0 )$

D) vertices: $( 0 , - \sqrt { 10 } ) , ( 0 , \sqrt { 10 } )$

foci: $( 0 , - 2 \sqrt { 5 } ) , ( 0,2 \sqrt { 5 } )$

Quizplus · Accepted Answer

The given equation is in the form suggesting a horizontal hyperbola centered at the origin. The vertices are found by setting $y=0$, which gives $x = \pm \sqrt{10}$, and the foci are located at $(\pm c, 0)$ where $c^2 = a^2 + b^2$, and since $b^2 = 0$ in this case, $c = \pm \sqrt{10 + 0} = \pm 2\sqrt{5}$.

The Hyperbola 1 Locate a Hyperbola's Vertices and Foci - y=±x2−10y = \pm \sqrt { x ^ { 2 } - 10 }y=±x2−10​

The Hyperbola
1 Locate a Hyperbola's Vertices and Foci
- $y = \pm \sqrt { x ^ { 2 } - 10 }$