Results 1 to 5 of 5

Math Help - Ellipse Equation

  1. #1
    MHF Contributor
    Joined
    Jul 2008
    From
    NYC
    Posts
    1,489

    Ellipse Equation

    The graph of which equation forms an ellipse?
    (1) x^2 - y^2 = 9 (3) 2x^2 + y^2 = 8
    (2) 2x^2 + 2y^2 = 8 (4) xy = -8

    I tested myself on a textbook quiz and got this question wrong. I selected choice (2) but the correct answer is choice (3). What makes choice (3) correct?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Dec 2008
    From
    Auckland, New Zealand
    Posts
    189
    An ellipse has the equation: \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1.

    You can see that for equation 2, dividing by 2 gives x^2 + y^2 = 4. Because the coefficients of x^2 and y^2 are the same, this equation represents a circle.

    For equation 3, dividing by 8 gives \frac{x^2}{4} + \frac{y^2}{8} = 1
    The coefficients of x^2 and y^2 are different, and so this equation represents an ellipse
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Jul 2008
    From
    NYC
    Posts
    1,489

    Yes............

    Quote Originally Posted by nzmathman View Post
    An ellipse has the equation: \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1.

    You can see that for equation 2, dividing by 2 gives x^2 + y^2 = 4. Because the coefficients of x^2 and y^2 are the same, this equation represents a circle.

    For equation 3, dividing by 8 gives \frac{x^2}{4} + \frac{y^2}{8} = 1
    The coefficients of x^2 and y^2 are different, and so this equation represents an ellipse
    Yes, I can clearly see that now thanks to you.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    o_O
    o_O is offline
    Primero Espada
    o_O's Avatar
    Joined
    Mar 2008
    From
    Canada
    Posts
    1,407
    Technically, a circle is an ellipse - just a "special" case of one where the two foci happen to be at the same point (or in terms of nzmathman's equation, the "special" case where a = b)
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Joined
    Jul 2008
    From
    NYC
    Posts
    1,489

    yes...

    Quote Originally Posted by o_O View Post
    Technically, a circle is an ellipse - just a "special" case of one where the two foci happen to be at the same point (or in terms of nzmathman's equation, the "special" case where a = b)
    Yes, I read that a circle is a special type of circle in the textbook some months ago.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Equation of an ellipse.
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: July 23rd 2011, 04:28 AM
  2. Equation of an ellipse
    Posted in the Algebra Forum
    Replies: 4
    Last Post: February 23rd 2010, 05:36 AM
  3. Equation of an Ellipse
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: April 21st 2009, 07:11 PM
  4. help with ellipse equation
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: July 9th 2007, 03:46 AM
  5. One yes or no and one ellipse equation
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: June 7th 2006, 07:08 PM

Search Tags


/mathhelpforum @mathhelpforum