Find the center,vertices and foci of the hyperbola. $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 25 } = 1$
A)Center: (0,0) Vertices: $( 4,0 )$
Foci: $( \pm \sqrt { 41 } , 0 )$
B)Center: (0,0) Vertices: $$( - 4,0 )$$
Foci: $( - \sqrt { 41 } , 0 )$
C)Center: (0,0) Vertices: $( 4,0 )$
Foci: $( - \sqrt { 41 } , 0 )$
D)Center: (0,0) Vertices: $( 4,0 )$
Foci: $$( \sqrt { 41 } , 0 )$$
E)Center: (0,0) Vertices: $( \pm 4,0 )$
Foci: $( \pm \sqrt { 41 } , 0 )$

Question

Find the center,vertices and foci of the hyperbola.​ $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 25 } = 1$ ​
A)Center: (0,0) Vertices: $( 4,0 )$
Foci: $( \pm \sqrt { 41 } , 0 )$
B)Center: (0,0) Vertices: $$( - 4,0 )$$
Foci: $( - \sqrt { 41 } , 0 )$
C)Center: (0,0) Vertices: $( 4,0 )$
Foci: $( - \sqrt { 41 } , 0 )$
D)Center: (0,0) Vertices: $( 4,0 )$
Foci: $$( \sqrt { 41 } , 0 )$$
E)Center: (0,0) Vertices: $( \pm 4,0 )$
Foci: $( \pm \sqrt { 41 } , 0 )$

Quizplus · Accepted Answer

All of the options have the same center (0,0) so we can ignore that. 
We know that the vertices of a hyperbola are the points where the distance from the center to the curve is the longest. Looking at the options, we can see that option E has the widest spread between vertices, which makes it the most likely choice. 
To confirm this, we can also look at the foci of the hyperbola. The distance between the foci and center determines the shape of the hyperbola; the greater the distance, the more spread out the hyperbola will be. Again, option E has the largest distance between foci, confirming our choice.

Find the Center,vertices and Foci of the Hyperbola x216−y225=1\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 25 } = 116x2​−25y2​=1

Find the Center,vertices and Foci of the Hyperbola $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 25 } = 1$