Graph Hyperbolas Not Centered at the Origin
-$$( \mathrm { y } + 2 ) ^ { 2 } - 4 ( \mathrm { x } + 1 ) ^ { 2 } = 4$$
A) Center: $( - 1 , - 2 )$; Vertices: $( - 1 , - 4 )$ and $( - 1,0 )$; Foci: $( - 1 , - 2 - \sqrt { 5 } )$ and $( - 1 , - 2 + \sqrt { 5 } )$
B) Center: $( 1,2 )$; Vertices: $( 1,0 )$ and $( 1,4 )$; Foci: $( 1,2 - \sqrt { 5 } )$ and $( 1,2 + \sqrt { 5 } )$
C) Center: $( - 1 , - 2 )$; Vertices: $( 1 , - 2 )$ and $( - 1,2 )$; Foci: $( - 1 , - \sqrt { 5 } )$ and $( - 1 , \sqrt { 5 } )$
D) Center: $( - 1 , - 2 )$; Vertices: $( 0 , - 3 )$ and $( 0,1 )$; Foci: $( 0 , - 1 - \sqrt { 5 } )$ and $( 0 , - 1 + \sqrt { 5 } )$

Question

Quizplus · Accepted Answer

The equation $(y + 2)^2 - 4(x + 1)^2 = 4$ is in the form of a hyperbola not centered at the origin. The center is found by setting the expressions inside the parentheses to zero, giving $(-1, -2)$. The vertices and foci calculations are based on the standard form of a hyperbola equation, confirming choice A is correct.

Graph Hyperbolas Not Centered at the Origin - (y+2)2−4(x+1)2=4( \mathrm { y } + 2 ) ^ { 2 } - 4 ( \mathrm { x } + 1 ) ^ { 2 } = 4(y+2)2−4(x+1)2=4

Graph Hyperbolas Not Centered at the Origin
- $( \mathrm { y } + 2 ) ^ { 2 } - 4 ( \mathrm { x } + 1 ) ^ { 2 } = 4$