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


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



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.



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





cool cool cool

CPhill  Apr 2, 2018

20 Online Users

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.