Results 1 to 3 of 3

Math Help - Put a Conic Section into General Form

  1. #1
    Newbie
    Joined
    May 2008
    Posts
    18

    Question Put a Conic Section into General Form

    I have to put the ellipse with the equation ax^2+by^2+cx+dy+e=0 into standard form, \frac{(x-h)^2}{a}+\frac{(y-k)^2}{b}=1

    I have attached my work as a picture since it would take a long time to type in (I did it on Microsoft Office). Could anyone tell me if I am correct, and if not, where did I go wrong? Thanks!
    Attached Thumbnails Attached Thumbnails Put a Conic Section into General Form-ellipse-work.jpg  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    A riddle wrapped in an enigma
    masters's Avatar
    Joined
    Jan 2008
    From
    Big Stone Gap, Virginia
    Posts
    2,551
    Thanks
    11
    Awards
    1
    Quote Originally Posted by sleigh View Post
    I have to put the ellipse with the equation ax^2+by^2+cx+dy+e=0 into standard form, \frac{(x-h)^2}{a}+\frac{(y-k)^2}{b}=1

    I have attached my work as a picture since it would take a long time to type in (I did it on Microsoft Office). Could anyone tell me if I am correct, and if not, where did I go wrong? Thanks!
    Hi sleigh,

    After completing the square in the 4th row, you factored incorrectly in the 5th row.

    It should be:

    a\left(x+\frac{c}{2a}\right)^2+b\left(y+\frac{d}{2  b}\right)^2=-e+\frac{c^2}{4a}+\frac{d^2}{4b}

    Too bad the error came so early. Why on Earth would anyone want to do this, anyway?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    May 2008
    Posts
    18
    Quote Originally Posted by masters View Post
    Hi sleigh,

    After completing the square in the 4th row, you factored incorrectly in the 5th row.

    It should be:

    a\left(x+\frac{c}{2a}\right)^2+b\left(y+\frac{d}{2  b}\right)^2=-e+\frac{c^2}{4a}+\frac{d^2}{4b}

    Too bad the error came so early. Why on Earth would anyone want to do this, anyway?
    Does this error make the entire thing wrong? Even though I factored wrong, I don't think this affects the rest of the problem because I added the correct amount to the other side, and I do not expand the binomials after I factored them.

    I am doing this to program my calculator to put it into standard form and give all of the information. I have a program to do it in standard form, but I wanted it to work for general form, too. This way, for example, the x coorodinate of the vertex is \frac{-c}{2a}. This would work for the y coorodinate, a^2 term and b^2. I already did this for the parabola and circle, but I was unsure of this one. Thanks for your help!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. help needed with conic section and hyperbolas
    Posted in the Geometry Forum
    Replies: 1
    Last Post: April 30th 2010, 12:35 PM
  2. Prove the conic section is a hyperbola
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: October 30th 2009, 04:23 AM
  3. Replies: 4
    Last Post: August 23rd 2009, 10:24 PM
  4. Conic Section Application Problems
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: May 31st 2009, 06:21 PM
  5. Conic section
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: September 3rd 2008, 08:18 AM

Search Tags


/mathhelpforum @mathhelpforum