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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