Hyperbola Explanation

Find the center, vertices, foci, eccentricity, and asymptotes of the hyperbola with the given equation:

Question

Hyperbola Explanation

Find the center, vertices, foci, eccentricity, and asymptotes of the hyperbola with the given equation:

anonymous · Answer

$$\frac{ y^{2} }{ 25 }-\frac{ x^{2} }{ 144 } = 1$$

This is a practice problem from a website, and I'd like to know how to do all of this.

anonymous · Answer

@hero @ganeshie8 @dan815

anonymous · Answer

@thomaster

anonymous · Answer

@hartnn

ganeshie8 · Answer

see if this helps

dan815 · Answer

okay hmmm

dan815 · Answer

do a hyperbola have the foci in the same place as the ellipse

anonymous · Answer

Okay, so:
Vertical
No x intercepts
Y intercept: (0,-+25)
Vertices: (0,-+25)
LTA: 50
LCA: 288
Foci: 13
e > 1
Asymptotes: y = -+25/144x

anonymous · Answer

@ganeshie8

anonymous · Answer

idk dan

dan815 · Answer

ah ganeshie8's post cover it all

anonymous · Answer

Pretty cool chart, makes it easy. :D

anonymous · Answer

Give ganeshie a medal please.

dan815 · Answer

=]

dan815 · Answer

i give ganehie8 too many medals :)

anonymous · Answer

lol

ganeshie8 · Answer

$$\frac{ y^{2} }{ 25 }-\frac{ x^{2} }{ 144 } = 1$$

ganeshie8 · Answer

$$\frac{ y^{2} }{ 5^2 }-\frac{ x^{2} }{ 12^2 } = 1$$

ganeshie8 · Answer

$\large a = 5$,   
$\large b = 12$

ganeshie8 · Answer

$\large  c =  \sqrt{a^2+b^2} = \sqrt{5^2 + 12^2} = 13$

ganeshie8 · Answer

use the chart now :)

anonymous · Answer

Oh yeah, I have to square root them to get the actual equation to use.