Results 1 to 3 of 3

Thread: Find the center the length of the axes and eccentricity of ellipse.

  1. #1
    Banned
    Joined
    Dec 2008
    Posts
    67

    Find the center the length of the axes and eccentricity of ellipse.

    Find the center the length of the axes and eccentricity of ellipse.
    $\displaystyle 2x^2+3y^2-4x-12y+13=0$
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Lord of certain Rings
    Isomorphism's Avatar
    Joined
    Dec 2007
    From
    IISc, Bangalore
    Posts
    1,465
    Thanks
    6
    Quote Originally Posted by varunnayudu View Post
    Find the center the length of the axes and eccentricity of ellipse.
    $\displaystyle 2x^2+3y^2-4x-12y+13=0$

    $\displaystyle 2x^2+3y^2-4x-12y+13= 0$

    $\displaystyle 2(x^2 - 2x + 1)+3(y^2-4y+4) - 1 = 0$

    $\displaystyle 2(x-1)^2+3(y-2)^2 = 1$

    $\displaystyle \dfrac{(x-1)^2}{\frac12}+\dfrac{(y-2)^2}{\frac13} = 1$

    Now its in standard form, can you continue?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Grandad's Avatar
    Joined
    Dec 2008
    From
    South Coast of England
    Posts
    2,570
    Thanks
    1

    Ellipse

    Hi -

    Quote Originally Posted by varunnayudu View Post
    Find the center the length of the axes and eccentricity of ellipse.
    $\displaystyle 2x^2+3y^2-4x-12y+13=0$
    Complete the square for x:

    $\displaystyle 2x^2 - 4x = 2(x^2 - 2x)$

    $\displaystyle =2((x-1)^2-1)$

    $\displaystyle =2(x-1)^2-2$

    and for y:

    $\displaystyle 3y^2-12y =3(y^2-4y)$

    $\displaystyle =3((y-2)^2-4)$

    $\displaystyle =3(y-2)^2-12$

    So the equation can be re-written:

    $\displaystyle 2(x-1)^2-2+3(y-2)^2-12+13=0$

    i.e. $\displaystyle 2(x-1)^2 + 3(y-2)^2=1$

    Substitute $\displaystyle u=x-1$ and $\displaystyle v=y-2$:

    $\displaystyle 2u^2+3v^2=1$

    Re-arrange:

    $\displaystyle \frac{u^2}{(\frac{1}{\sqrt{2}})^2} + \frac{v^2}{(\frac{1}{\sqrt{3}})^2}=1$

    OK from here?

    Grandad
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Eccentricity of ellipse
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: Dec 5th 2011, 04:33 AM
  2. Replies: 4
    Last Post: May 7th 2010, 10:23 AM
  3. Find the center, vertices, foci and eccentricity
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: May 5th 2010, 09:41 AM
  4. Is the eccentricity of this ellipse correct?
    Posted in the Algebra Forum
    Replies: 1
    Last Post: Aug 22nd 2009, 08:19 AM
  5. ellipse axes
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Oct 19th 2006, 04:16 AM

Search tags for this page

Click on a term to search for related topics.

Search Tags


/mathhelpforum @mathhelpforum