Results 1 to 2 of 2

Math Help - Solve Linear equation with second degree to get Quadratic eqn

  1. #1
    Newbie
    Joined
    May 2009
    Posts
    13

    Solve Linear equation with second degree to get Quadratic eqn

    Hi,

    How to solve following equation and get a quadratic equation in X or Y

    Ellipse equation with centre (h1,k1) ,major axis(a) and minor axis distance (b)
    (X-h1)^ 2 / a^2 + (Y-k1)^2 /b^2 = 1 ------------------ I

    and

    Circle equation with radius R and centre (h2,k2)

    (X-h2)^2 + (Y-k2)^2 = R^2 -------------------------II


    Rajee
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,298
    Thanks
    1276
    Quote Originally Posted by mrajee View Post
    Hi,

    How to solve following equation and get a quadratic equation in X or Y

    Ellipse equation with centre (h1,k1) ,major axis(a) and minor axis distance (b)
    (X-h1)^ 2 / a^2 + (Y-k1)^2 /b^2 = 1 ------------------ I

    and

    Circle equation with radius R and centre (h2,k2)

    (X-h2)^2 + (Y-k2)^2 = R^2 -------------------------II


    Rajee
    What are you asking? You will NOT get a quadratic equation by solving those equations- they are quadratic. And, contrary to your title, there are no linear equations here.

    If you do mean "solve following equation" which variable do you want to solve for?

    To solve I for X, subtract (Y- Y1)^2/b^2 from both sides to get (X-X1)/a^2= 1- (Y-Y1)^2/b^2. Multiply both sides by a^2 to get (X-X1)^2= a^2(1- (Y-Y1)^2/b^2). Take the square root of both sides to get X- X1= +/- a sqrt(1- (Y-Y1)^2/b^2). Finally add X1 to both sides to get X= X1 +/- a sqrt{1- (Y-Y1)^2/b^2). That is neither a "linear" nor a "quadratic" equation.

    To solve it for Y, Do the same thing but keep Y on the left side rather than X.

    To solve II for X or Y, pretty much the same thing but easier- you don't have an "a" or "b" to worry about.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: September 23rd 2011, 06:49 AM
  2. Solve this quadratic equation
    Posted in the Algebra Forum
    Replies: 1
    Last Post: April 15th 2010, 08:03 AM
  3. Replies: 4
    Last Post: December 29th 2008, 08:50 AM
  4. Solve quadratic equation for x
    Posted in the Algebra Forum
    Replies: 1
    Last Post: September 11th 2008, 05:59 AM
  5. Solve this Quadratic Equation
    Posted in the Algebra Forum
    Replies: 7
    Last Post: April 5th 2008, 05:20 AM

Search Tags


/mathhelpforum @mathhelpforum