Find the equation of a hyperbola with foci of

(0,8), and (0,-8)

and Asymptotes of

y=4x and y=-4x

1. 👍
2. 👎
3. 👁
1. 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

1. 👍
2. 👎
2. correction:
using x^2/a^2 = y^2/b^2 = -1 should say

using x^2/a^2 - y^2/b^2 = -1

1. 👍
2. 👎
3. 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

1. 👍
2. 👎
4. <..but wouldn't 32^2 be 1024>

of course, good for you for catching that.

let's blame it on a "senior moment"

1. 👍
2. 👎

## Similar Questions

1. ### precalculus

Find the standard form of the equation of the hyperbola with vertices (0±3) and asymptotes (y=±3/2x)

2. ### precalculus

find an hyperbola equation with foci (0, +/-8) and asymptotes; y=+/-1/2x?

3. ### Precalc

Find the standard form of the equation of the hyperbola with the given characteristics. foci: (±4, 0) asymptotes: y= +/- 3x

4. ### algebra

HYPERBOLA Q!! Find an equation for a horizontal hyperbola with vertices that are 20 units apart from each other and foci 30 units apart each other?? im lost on this any help is appreciated !!!

1. ### pre-cal

find an equation for the hyperbola vertices (3,0),(3,4) asymptotes:y=2/3,y=4-2/3x

2. ### precalc

find the standard form of the hyperbola, the center and vertices given the foci (0, -+8) and asymptotes at y=4x

3. ### pre-calculus

how to find the equation of a parabola given foci(-7,-17), (-7,17 ),the absolute value of the difference of the distances of any point from the foci is 24

4. ### Pre-calc

Heres the equation: (x^2)-(4y^2)-(4x)+(24y)-(36)=0 Your supposed to find the coordinates of the center, foci, and vertices, and the equations of the asymptotes of its graph. So first you complete the square right? (x^2

1. ### Math

Find the vertices, center, asymptotes, and foci of the ellipse and sketch its graph: 9x^2-4y^2-18x+8y+41=0

2. ### math

Find equations for the asymptotes of the hyperbola x2/9 - y2/81 = 1 Rewrite the equation as (x/3)^2 - (y/9)^2 = 1 When both x and y are very large in absolute value, the "1" on the right is negligible in comparison, so y/9

3. ### Algebra

HELP! I am not sure how I would even start this problem or solve it. A hyperbola with a horizontal transverse axis contains the point at (4, 3). The equations of the asymptotes are y-x=1 and y+x=5 Write an equation for the

4. ### maths

Give the equation of the hyperbola is 9x^2-4y^2=36.find (i)center and vertices (ii)foci and eccentricity (iii)equation of assymptotes