Identify the vertices and the foci.
-$$x ^ { 2 } - \frac { ( y + 5 ) ^ { 2 } } { 3 } = 1$$
A) vertices: $( 1,5 ) , ( - 1,5 )$
foci: $( 2,5 ) , ( - 2,5 )$
B) vertices: $( 1 , - 5 ) , ( - 1 , - 5 )$
foci: $( 2 , - 5 ) , ( - 2 , - 5 )$
C) vertices: $( 0 , - 5 + \sqrt { 3 } ) , ( 0 , - 5 - \sqrt { 3 } )$
foci: $( 0 , - 7 ) , ( 0 , - 3 )$
D) vertices: $( 0,5 + \sqrt { 3 } ) , ( 0,5 - \sqrt { 3 } )$
foci: $( 0,7 ) , ( 0,3 )$

Question

Quizplus · Accepted Answer

The given equation is in the form of a hyperbola centered at $(0, -5)$ with a horizontal transverse axis. The vertices are $(\pm 1, -5)$ and the foci, given by $c = \sqrt{a^2 + b^2}$ where $a^2 = 1$ and $b^2 = 3$, are $(\pm 2, -5)$.

Identify the Vertices and the Foci x2−(y+5)23=1x ^ { 2 } - \frac { ( y + 5 ) ^ { 2 } } { 3 } = 1x2−3(y+5)2​=1

Identify the Vertices and the Foci $x ^ { 2 } - \frac { ( y + 5 ) ^ { 2 } } { 3 } = 1$