what is the standard-form equation of the hyperbola with vertices (0,+or- 4) and foci (0, +or- 5)?

what is the difference between a parabola and a hyperbola

under what circumstances are the asymptotes of a hyperbola perpendicular

OfficialBubbleTanks
Apr 2, 2018

#1**+1 **

foci (0, - 5) and (0, 5)

vertices (0, 4) and (0, -4)

Since the vertices and focus are on the y axis and the center is (0,0).....this hperbola will have the form

y^2 x^2

___ - ____ = 1

a^2 b^2

a = 4

c =5

and b = √[5^2 - 4^2 ] = 3

So....we have the form

y^2 x^2

___ - _____ = 1

16 9

Here's the graph : https://www.desmos.com/calculator/yq7wtlrut2

Parabola

Formally, a parabola is defined as follows: For a given point, called the focus, and a given line not through the focus, called the directrix, a parabola is the locus of points such that the distance to the focus equals the distance to the directrix.

Hyperbola

Formally, a hyperbola can be defined as follows: For two given points, the foci, a hyperbola is the locus of points such that the difference between the distances to each focus is constant.

The asypmtotes of a hyperbola will be perpendicular when a = b

See here as an example : https://www.desmos.com/calculator/lahqwjj2fk

CPhill
Apr 2, 2018