Adv. Algebra- Conics

posted by .

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!!!

  • Adv. Algebra- Conics -

    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

  • Adv. Algebra- Conics -

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

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

  • Adv. Algebra- Conics -

    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

  • Adv. Algebra- Conics -

    <..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

First Name
School Subject
Your Answer

Similar Questions

  1. Pre-calculus-ck answers

    Identify the graph of the equation 4x^2-25y^2=100. Then write the equation of the translated graph for T(5,-2) in general form. Answer: hyperbola; 4(x-5)^2 -25(y+2)^2=100 2)Find the coordinates of the center, the foci, and the vertices, …
  2. 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
  3. math 30 conics

    Hi i was given the equation (y-2)^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 …
  4. Precalc

    Find the standard form of the equation of the hyperbola with the given characteristics. foci: (±4, 0) asymptotes: y= +/- 3x
  5. algebra 2

    Graph the equation. Identify the vertices, foci, and asymptotes of the hyperbola. Y^2/16-x^2/36=1 I think....vertices (0,4),(0,-4) foci?
  6. 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.
  7. 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)
  8. precalculus

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

    For the following equation of a hyperbola determine the center, vertices, foci, and asymptotes?
  10. Algebra2

    What are the vertices, foci, and asymptotes of the hyperbola with the equation 16x^2-4y^2=64?

More Similar Questions