Results 1 to 5 of 5

Math Help - Equation of an ellipse.

  1. #1
    Member
    Joined
    Apr 2009
    From
    Jerusalem - Israel
    Posts
    108

    Equation of an ellipse.

    find h in the ellipse hy^2-4x^2+h=0 if a^2+b^2=10
    where a, b are the axes of the ellipse.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5

    Re: Equation of an ellipse.

    Quote Originally Posted by razemsoft21 View Post
    find h in the ellipse hy^2-4x^2+h=0 if a^2+b^2=10
    where a, b are the axes of the ellipse.
    There is no value of h for which hy^2-4x^2+h=0 is an ellipse. h > 0 defines a hyperbola, h < 0 is the null set, h = 0 is a line.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor Siron's Avatar
    Joined
    Jul 2011
    From
    Norway
    Posts
    1,250
    Thanks
    20

    Re: Equation of an ellipse.

    I agree with mr.fantastic, but let h>0 then you have a hyperbola. You know the equation of a hyperbola in general:
    \frac{x^2}{a^x}-\frac{y^2}{b^2}=1

    Now, for h>0:
    Consider the given equation:
    hy^2-4x^2+h=0
    \Leftrightarrow hy^2-4x^2=-h
    \Leftrightarrow \frac{hy^2}{-h}-\left(\frac{4x^2}{-h}\right)=1 (because h>0, we may divide the sides by h and also -h)
    \Leftrightarrow \frac{x^2}{\frac{h}{4}}-y^2=1

    Now we have the standard equation of the hyperbola and that means you can determine a^2 and b^2.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5

    Re: Equation of an ellipse.

    Quote Originally Posted by Siron View Post
    I agree with mr.fantastic, but let h>0 then you have a hyperbola. You know the equation of a hyperbola in general:
    \frac{x^2}{a^x}-\frac{y^2}{b^2}=1

    Now, for h>0:
    Consider the given equation:
    hy^2-4x^2+h=0
    \Leftrightarrow hy^2-4x^2=-h
    \Leftrightarrow \frac{hy^2}{-h}-\left(\frac{4x^2}{-h}\right)=1 (because h>0, we may divide the sides by h and also -h)
    \Leftrightarrow \frac{x^2}{\frac{h}{4}}-y^2=1

    Now we have the standard equation of the hyperbola and that means you can determine a^2 and b^2.
    I had assumed as much. And I suppose the OP giving Thanks is implicit confirmation of what the correct question was meant to be.

    However, I was hoping that the OP would explicitly state the correction to his/her original question (which was the intention of my post).
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,725
    Thanks
    1478

    Re: Equation of an ellipse.

    If the "-" was simply 'misplaced' and the equation was hy^2+ 4x^2- h= 0, then we can rewrite it as
    4x^2+ hy^2= h and, dividing by h, \frac{x^2}{\frac{h}{4}}+ y^2= 1 which, for h> 0, is an ellipse. Assuming that "a" is the length of the semi-axis along the x-axis and "b" the length of the sem-axis along the y-axis, we have a^2= \frac{h}{4} and b^2= 1.

    From the first equation h= 4a^2 and from the second b^2= 1. a^2= 10- b^2= 9 so h= 4(9)= 36.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Equation for an ellipse
    Posted in the Geometry Forum
    Replies: 2
    Last Post: May 22nd 2010, 02:36 PM
  2. Equation of an ellipse
    Posted in the Algebra Forum
    Replies: 4
    Last Post: February 23rd 2010, 05:36 AM
  3. Equation of a n ellipse??
    Posted in the Algebra Forum
    Replies: 1
    Last Post: March 28th 2009, 04:02 PM
  4. Ellipse Equation
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: January 6th 2009, 06:16 AM
  5. help with ellipse equation
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: July 9th 2007, 03:46 AM

Search Tags


/mathhelpforum @mathhelpforum