Results 1 to 2 of 2

Math Help - Equation of a conic

  1. #1
    Junior Member
    Joined
    Mar 2008
    From
    Ohio
    Posts
    26

    Exclamation Equation of a conic

    Trying to figure out the whole "conic sections" thing... Here's the problem I'm stuck on: "Write the equation of the conic in standard form, and classify it as a circle, a parabola, an ellipse, or a hyperbola: 3x^2-2y^2+24x+12y+24=0"

    Also, if anyone just knows any basic "steps" to follow when trying to find the foci, directerix, vertices, equations, etc, generally speaking, that would be IMMENSELY helpful! I've got a test tonight and I'm pretty confused!

    Thanks in advance for any help!!!!!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78

    Conics

    A good first step is to complete the square on each of the variables.

    3x^2+24x-2y^2+12y=-24

    factoring and completing the square we get.

    3(x^2+8x+16)-2(y^2-6y+9)=-24+3(16)+(-2)(9)

    factoring and combining like terms

    3(x+4)^2-2(y-3)^2=6

    divide everything by 6 to put into standart form.

    \frac{(x+4)^2}{(\sqrt{2})^2}-\frac{(y-3)^2}{(\sqrt{3})^2}=1

    This is the standard form of a hyperbola.

    \frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1

    The foci can be found using the equation c=foci

    c^2=b^2+a^2 so the foci are at c=\pm \sqrt{5}

    they are located at the points (\pm \sqrt{5},0)

    The asymptotes of the hyperbola can be found with the equation

    y=\pm \frac{b}{a}x=\pm \frac{\sqrt{3}}{\sqrt{2}}

    Good luck.

    P.S. The formula for foci is different for each conic section.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Matrix equation of a conic.
    Posted in the Pre-Calculus Forum
    Replies: 6
    Last Post: September 10th 2010, 04:12 AM
  2. Conic Equation
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: May 12th 2010, 08:32 AM
  3. Matrix Conic Equation
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: August 18th 2009, 11:23 PM
  4. simplify conic equation
    Posted in the Pre-Calculus Forum
    Replies: 6
    Last Post: July 5th 2008, 09:43 PM
  5. General Equation of a Conic
    Posted in the Algebra Forum
    Replies: 4
    Last Post: March 18th 2008, 12:37 PM

Search Tags


/mathhelpforum @mathhelpforum