Adv. Algebra Conics
posted by Paragon .
Find the equation of a hyperbola with foci of
(0,8), and (0,8)
and Asymptotes of
y=4x and y=4x
Please show work!!!

In a hyperbola with centre at the origin the equation of the asymptote is y = ±(b/a)x.
so b/a = 4 or b = 4a
Also c = 8
then in a^2 + b^2 = c^2 for a hyperbola
a^2 + 16a^2 = 64
17a^2 = 64
a = 8/√17
then b=32/√17
using x^2/a^2 = y^2/b^2 = 1
x^2/(64/17)  y^2/(32/17) = 1
17x^2 /64  17y^2 /64 = 1 
correction:
using x^2/a^2 = y^2/b^2 = 1 should say
using x^2/a^2  y^2/b^2 = 1 
Wow it's that easy. I was making it harder that it is.
I think that's how you set it up, but wouldn't 32^2 be 1024 
<..but wouldn't 32^2 be 1024>
of course, good for you for catching that.
let's blame it on a "senior moment"
Respond to this Question
Similar Questions

Precalculusck answers
Identify the graph of the equation 4x^225y^2=100. Then write the equation of the translated graph for T(5,2) in general form. Answer: hyperbola; 4(x5)^2 25(y+2)^2=100 2)Find the coordinates of the center, the foci, and the vertices, … 
College Algebra.
Find the equation in standard form of the hyperbola that satisfies the stated condition. Foci (0,5) and (0,5), asymptotes y = x and y =x 
math 30 conics
Hi i was given the equation (y2)^2  x^2/4 =1. I need to find the center, vertices and asymptotes of this hyperbola. I found the center (0,2) and the vertices were tricky but I think they are (0,1) (0,3) but I'm having trouble finding … 
Precalc
Find the standard form of the equation of the hyperbola with the given characteristics. foci: (±4, 0) asymptotes: y= +/ 3x 
algebra 2
Graph the equation. Identify the vertices, foci, and asymptotes of the hyperbola. Y^2/16x^2/36=1 I think....vertices (0,4),(0,4) foci? 
College algebra
Find the standard form of the equation of the hyperbola with the given characteristics. Foci:(+4,0) or (4,0) Asymptotes: y=4x or y=4x. 
Math/ Algebra
Find an equation for the hyperbola described: 1) Vertices at (0,+/ 10); asymptotes at y= 5/3x 2) Vertices at (+5,0); foci at (+6,0) 
precalculus
find an hyperbola equation with foci (0, +/8) and asymptotes; y=+/1/2x? 
Algebra
For the following equation of a hyperbola determine the center, vertices, foci, and asymptotes? 
Algebra2
What are the vertices, foci, and asymptotes of the hyperbola with the equation 16x^24y^2=64?