Results 1 to 5 of 5

Math Help - Identifying a conic.

  1. #1
    Junior Member
    Joined
    Mar 2010
    Posts
    49

    Identifying a conic.

    Here is a question that I believe that I might have worked out partially, but I have one small sticking point that is really throwing me.

    The question:
    Identify the following conic. That is, is it a circle, parabola, hyperbola, or ellipse?
    Show why.
    Equation:
    x^2-4y^2-4x-24y=48

    My answer so far:
    x^2-4y^2-4x-24y=48 can be identified as a hyperbola by executing the following steps:
    Rearrange the terms:
    [Math](x^2-4c+a)+(-4y^2-24y+b)~48-a+b[/tex]
    Complete the square:
    (this is where my problem lies, I'm not quite sure that my result is correct.)
    (x^2-4c+1)-4(y^2+6t+4)=48+1-16

    I realize that my answer is incomplete, but I can't quite figure out where I'm going wrong.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Dec 2010
    Posts
    470
    In order to complete the square:
    you need a=4 and b=-36
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,790
    Thanks
    1531
    Quote Originally Posted by quikwerk View Post
    Here is a question that I believe that I might have worked out partially, but I have one small sticking point that is really throwing me.

    The question:
    Identify the following conic. That is, is it a circle, parabola, hyperbola, or ellipse?
    Show why.
    Equation:
    x^2-4y^2-4x-24y=48

    My answer so far:
    x^2-4y^2-4x-24y=48 can be identified as a hyperbola by executing the following steps:
    Rearrange the terms:
    [Math](x^2-4c+a)+(-4y^2-24y+b)~48-a+b[/tex]
    Complete the square:
    (this is where my problem lies, I'm not quite sure that my result is correct.)
    (x^2-4c+1)-4(y^2+6t+4)=48+1-16
    You mean "4x", not "4c" but the problem appears to be that you do not know how to "complete the square". Why did you add "1" and "4"?
    A "perfect square" is of the form (x- a)^2= x^2- 2ax+ a^2. Compare that to x^2- 4x+ ?. Where you have "4x", the general formula has "2ax". Okay, for those to be the same, you must have 4= 2a. What is "a"? What is " a^2"? That's what you want to add to both sides of the equation.

    You have the same problem with the y term. -4y^2- 24y= -4(y^2+ 6y) (Not 6t. You seem awfully careless with what you write!)
    Now compare (y+ a)^2= y^2+ 2ay+ a^2 and y^2+ 6y. You must have 2a= 6 so what is a? What is a^2? That is what you want to add, not "4".

    I realize that my answer is incomplete, but I can't quite figure out where I'm going wrong.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Mar 2010
    Posts
    49
    Quote Originally Posted by HallsofIvy View Post
    You mean "4x", not "4c" but the problem appears to be that you do not know how to "complete the square". Why did you add "1" and "4"?
    A "perfect square" is of the form (x- a)^2= x^2- 2ax+ a^2. Compare that to x^2- 4x+ ?. Where you have "4x", the general formula has "2ax". Okay, for those to be the same, you must have 4= 2a. What is "a"? What is " a^2"? That's what you want to add to both sides of the equation.

    You have the same problem with the y term. -4y^2- 24y= -4(y^2+ 6y) (Not 6t. You seem awfully careless with what you write!)
    Now compare (y+ a)^2= y^2+ 2ay+ a^2 and y^2+ 6y. You must have 2a= 6 so what is a? What is a^2? That is what you want to add, not "4".
    I apologize for all the typos, the internet at my house is down at the moment, so I am using my smartphone to post thus the keyboard spaces out on me and puts a "c" where I mean "x"....
    Thanks for your help, though! I'm going to work it out again with your advice and report back with my results.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,749
    Thanks
    649
    Hello, quikwerk!

    Identify the following conic: circle, parabola, hyperbola, or ellipse.
    Show why.

    . . . x^2-4y^2-4x-24y\:=\:48

    If it asks us to "Identify" (only), and not about the center or axes,
    . . the answer is hyperbola.


    There is an "eyeball" approach to identifying conics.


    One general form is: . Ax^2 + By^2 + Cx + Dy + E \:=\:0

    . . If A = 0 or B = 0: parabola.

    . . If A = B: circle.

    . . If \,A and \,B have the same sign and A \ne B: ellipse.

    . . If AB < 0 ( \,A and \,B have opposite signs): hyperbola.



    You may wish to complete-the-square, etc. to determine if we have:

    . . a degenerate conic, such as: . (x-2)^2 + (y-3)^2 \:=\:0

    . . or an "imaginary" conic, such as: . \dfrac{x^2}{9} + \dfrac{y^2}{4} \:=\:-1

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Identifying the sequence
    Posted in the Number Theory Forum
    Replies: 5
    Last Post: April 22nd 2012, 11:21 AM
  2. Need Help Identifying Technique
    Posted in the Calculus Forum
    Replies: 2
    Last Post: October 14th 2011, 07:40 AM
  3. Need help identifying graphs
    Posted in the Algebra Forum
    Replies: 1
    Last Post: July 11th 2010, 09:30 PM
  4. Identifying a conic.
    Posted in the Algebra Forum
    Replies: 7
    Last Post: February 22nd 2010, 05:36 PM
  5. Help please: identifying data type
    Posted in the Advanced Statistics Forum
    Replies: 5
    Last Post: November 26th 2006, 02:19 PM

Search Tags


/mathhelpforum @mathhelpforum