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
___ - ____ = 1
a = 4
and b = √[5^2 - 4^2 ] = 3
So....we have the form
___ - _____ = 1
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