Math Is Fun Forum

Kiran

Member

Registered: 2006-11-15

Posts: 177

did the problem but need help with the graph

consider the hyperbola 16x^2 - 4y^2 + 64 = 0
write this equation in standard form and give the coordinates of the vertices and the equations of the asymptotes. then graph.

16x^2 - 4y^2 = 64

16x^2 / 64   -   4y^2 / 64   = 1
x^2 / 0.25   -   y^2 / 0.0625  =  1  < simplified

Let x = 0
y^2 / 0.25 - (0)^2 / 0.0625 = 1
y = +- 0.5

let y = 0
(0)^2 / 0.25   -  x^2 / 0.0625  =  1
x = +- 0.25

now teh coordinates are :
(0,0.5) (0,-0.5)
(0.25,0) (-0.25,0)

Asymptotes :
y = 0.5/0.25 x

and

y = - 0.5/0.25 x

now how do you graph the coordinates ?

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MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,711

Re: did the problem but need help with the graph

16x^2 - 4y^2 + 64 = 0
4y^2 = 16x^2 + 64
y^2 = 4x^2 + 16
y = ± √(4x^2 + 16)

Plot of sqrt(4x^2+16) vs -sqrt(4x^2+16)

You might have gone wrong: "/ 0.25" should be "/4" or "×0.25", likewise for "/ 0.0625"

The graph should help you now.

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman