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