Results 1 to 8 of 8

Math Help - Classify an equation

  1. #1
    Newbie
    Joined
    Dec 2009
    Posts
    11

    Classify an equation

    how do i tell if an equation is a circle, parabola, an ellipse, or hyperbola?

    an example is 5y^2-9y-12x^2-3x+6=0

    what do i look at to determine its geometry?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,623
    Thanks
    428
    Quote Originally Posted by vanessa123 View Post
    how do i tell if an equation is a circle, parabola, an ellipse, or hyperbola?

    an example is 5y^2-9y-12x^2-3x+6=0

    what do i look at to determine its geometry?
    Ay^2 - Bx^2 ... hyperbola

    Ay^2 + Bx^2 ... ellipse (circle if A = B)

    Ay \pm Bx^2 or Ay^2 \pm Bx ... parabola
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,829
    Thanks
    123
    Quote Originally Posted by vanessa123 View Post
    how do i tell if an equation is a circle, parabola, an ellipse, or hyperbola?

    an example is 5y^2-9y-12x^2-3x+6=0

    what do i look at to determine its geometry?
    Since the leading factors of the squares are different (value and sign) and there aren't any summands containing x \cdot y , this equation describes a hyperbola.

    If the axes of the conic section are parallel to the coordinate axes, you can determine the kind of conic by:

    1. The leading factors of the squares are both positive and equal: It's a circle.

    2. The leading factors of the squares are positive but unequal: It's an ellipse.

    3. The leading factors of the squares are different in value and sign: It's a hyperbola.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Dec 2009
    Posts
    11
    ok well i cant figure out if 21x^2+24xy-11y2=375 is a hyperbola or an ellipse because when i graphed it ...it ALMOST formed an ellipse but there was a gap that seperated it.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by vanessa123 View Post
    ok well i cant figure out if 21x^2+24xy-11y2=375 is a hyperbola or an ellipse because when i graphed it ...it ALMOST formed an ellipse but there was a gap that seperated it.
    The gap will be an artefact of the resolution of the calculator's graphics (number and size of pixels).
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Dec 2009
    Posts
    11
    Quote Originally Posted by mr fantastic View Post
    The gap will be an artefact of the resolution of the calculator's graphics (number and size of pixels).
    im sorry i still dont quite understand? so is it an ellipse? because it sure does look like one, the only thing that is causing me to second guess my self is the gaps.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,623
    Thanks
    428
    graph of 21x^2+24xy-11y^2=375 ...
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by skeeter View Post
    graph of 21x^2+24xy-11y^2=375 ...
    Indeed: http://www.wolframalpha.com/input/?i...1y%5E2+%3D+375.

    That's what I get for taking things on face value and not checking ....
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Classify the graph of the equation
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 7th 2011, 01:27 PM
  2. Where to classify that problem?
    Posted in the Advanced Math Topics Forum
    Replies: 1
    Last Post: November 10th 2011, 12:40 AM
  3. Classify the beam
    Posted in the Geometry Forum
    Replies: 0
    Last Post: September 15th 2010, 08:52 AM
  4. Classify Equation
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 2nd 2008, 11:59 PM
  5. Classify the following as the equation...
    Posted in the Pre-Calculus Forum
    Replies: 7
    Last Post: September 1st 2007, 11:35 AM

Search Tags


/mathhelpforum @mathhelpforum