Results 1 to 8 of 8

Math Help - Classify the following as the equation...

  1. #1
    Junior Member
    Joined
    Aug 2007
    Posts
    58

    Classify the following as the equation...

    Classify the following as the equation of a line, parabola, ellipse, hyperbola, or circle.

    What would be the easiest way to do this?!

    Here are the equations:

    x^2-20x=-y^2-6y
    and
    13x^2+13y^2-26x+52y=-78
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Oct 2006
    Posts
    679
    Awards
    1

    Re:

    Quote Originally Posted by deathtolife04 View Post
    Classify the following as the equation of a line, parabola, ellipse, hyperbola, or circle.

    What would be the easiest way to do this?!

    Here are the equations:

    x^2-20x=-y^2-6y
    RE:

    This is a circle
    Attached Thumbnails Attached Thumbnails Classify the following as the equation...-graph-8.jpg  
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,843
    Thanks
    320
    Awards
    1
    Quote Originally Posted by deathtolife04 View Post
    Classify the following as the equation of a line, parabola, ellipse, hyperbola, or circle.

    What would be the easiest way to do this?!

    Here are the equations:

    x^2-20x=-y^2-6y
    and
    13x^2+13y^2-26x+52y=-78
    Are there any of these that you can do? If not you need a serious review!

    You need to put the equations in terms of standard form by completing the square. For the first one:
    x^2-20x=-y^2-6y

    (x^2 - 20x) + (y^2 + 6y) = 0

    (x^2 - 20x + 10^2 - 10^2) + (y^2 + 6y + 3^2 - 3^2) = 0

    (x^2 - 20x + 10^2) + (y^2 + 6y + 3^2) =  10^2 + 3^2

    (x - 10)^2 + (y + 3)^2 = 109

    You tell me what kind of curve this is.

    As far as 13x^2+13y^2-26x+52y=-78 is concerned you have a typo. This is not a valid equation for real numbers.

    -Dan
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Aug 2007
    Posts
    58
    Quote Originally Posted by topsquark View Post
    Are there any of these that you can do? If not you need a serious review!

    You need to put the equations in terms of standard form by completing the square. For the first one:
    x^2-20x=-y^2-6y

    (x^2 - 20x) + (y^2 + 6y) = 0

    (x^2 - 20x + 10^2 - 10^2) + (y^2 + 6y + 3^2 - 3^2) = 0

    (x^2 - 20x + 10^2) + (y^2 + 6y + 3^2) =  10^2 + 3^2

    (x - 10)^2 + (y + 3)^2 = 109

    You tell me what kind of curve this is.

    As far as 13x^2+13y^2-26x+52y=-78 is concerned you have a typo. This is not a valid equation for real numbers.

    -Dan
    so that would be a circle then, right?

    why is the second one not a valid equation?

    is it because there's no "xy"?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,829
    Thanks
    123
    Quote Originally Posted by deathtolife04 View Post
    Classify the following as the equation
    ...
    13x^2+13y^2-26x+52y=-78
    Hello,

    as topsquark told you this equation is unvalid:

    13(x^2-2x+1)+13(y^2+4y+4)=-78+13+52 completing the squares and dividing by 13:

    (x-1)^2+(y+2)^2=-1

    The LHS of the equation would describe a circle with the centre at C(1, -2) but the RHS has to be a square. And a square never is negative. So ... see above.

    If and only if your equation reads: 13x^2+13y^2-26x+52y=78 then you'll get:

    (x-1)^2+(y+2)^2=11 that means the circle has a radius of \sqrt{11}
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    Joined
    Apr 2005
    Posts
    1,631
    Quote Originally Posted by deathtolife04 View Post
    Classify the following as the equation of a line, parabola, ellipse, hyperbola, or circle.

    What would be the easiest way to do this?!

    Here are the equations:

    x^2-20x=-y^2-6y
    and
    13x^2+13y^2-26x+52y=-78
    I don't know if you have studied yet all those: line, parabola, ellipse, hyperbola, circle. If yes, then you may understand my answer. If not all of them yet, then you will not fully understand my answer.

    Line.
    It is linear or of degree 1. Meaning, the x or the y have exponents of 1 only.
    It is in the form, y = Ax +B. Or, Ax +By +C = 0.

    Parabola.
    It is quadratic, or of degree 2. One of the variables is of degree 1 only, though.
    It is in the expanded form, y = Ax^2 +Bx +C. Or x = Ay^2 +By +C.

    Circle.
    It is quadratic, or of degree 2. Both variables are in degree 2. The coefficients of the two squared variables are equal or the same. It is the sum of the two squared variables, etc.
    In its expanded form, Ax^2 +Ay^2 +Bx +Cy +D = 0
    See that Ax^2 + Ay^2 ?

    Ellipse.
    It is quadratic, or of degree 2. Both variables are in degree 2. The coefficients of the two squared variables are unequal or not the same. It is the sum of the two squared variables, etc.
    In its expanded form, Ax^2 +By^2 +Cx +Dy +E = 0
    See that Ax^2 + By^2 ?

    Hyperbola.
    It is quadratic, or of degree 2. Both variables are in degree 2. The coefficients of the two squared variables may be equal or not equal. It is the subtraction of the two squared variables, etc.
    In its expanded form, Ax^2 -Ay^2 +Bx +Cy +D = 0
    Or, Ax^2 -By^2 +Cx +Dy +E = 0
    See those Ax^2 -Ay^2, or Ax^2 -By^2 ?
    ----Sometimes it has the "xy" term in the expanded form, even if the squared variables as not in there. Meaning, if you see a quadratic equation with an "xy" term, sum or subtraction, the equation is hyperbola.

    -------------------------------
    So, the two equations in your question here are both circles, although the last one is imaginary because the sum of two squared quantities (after completing the squares) cannot be negative. --------answer.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,843
    Thanks
    320
    Awards
    1
    Quote Originally Posted by ticbol View Post
    I don't know if you have studied yet all those: line, parabola, ellipse, hyperbola, circle. If yes, then you may understand my answer. If not all of them yet, then you will not fully understand my answer.

    Line.
    It is linear or of degree 1. Meaning, the x or the y have exponents of 1 only.
    It is in the form, y = Ax +B. Or, Ax +By +C = 0.

    Parabola.
    It is quadratic, or of degree 2. One of the variables is of degree 1 only, though.
    It is in the expanded form, y = Ax^2 +Bx +C. Or x = Ay^2 +By +C.

    Circle.
    It is quadratic, or of degree 2. Both variables are in degree 2. The coefficients of the two squared variables are equal or the same. It is the sum of the two squared variables, etc.
    In its expanded form, Ax^2 +Ay^2 +Bx +Cy +D = 0
    See that Ax^2 + Ay^2 ?

    Ellipse.
    It is quadratic, or of degree 2. Both variables are in degree 2. The coefficients of the two squared variables are unequal or not the same. It is the sum of the two squared variables, etc.
    In its expanded form, Ax^2 +By^2 +Cx +Dy +E = 0
    See that Ax^2 + By^2 ?

    Hyperbola.
    It is quadratic, or of degree 2. Both variables are in degree 2. The coefficients of the two squared variables may be equal or not equal. It is the subtraction of the two squared variables, etc.
    In its expanded form, Ax^2 -Ay^2 +Bx +Cy +D = 0
    Or, Ax^2 -By^2 +Cx +Dy +E = 0
    See those Ax^2 -Ay^2, or Ax^2 -By^2 ?
    ----Sometimes it has the "xy" term in the expanded form, even if the squared variables as not in there. Meaning, if you see a quadratic equation with an "xy" term, sum or subtraction, the equation is hyperbola.

    -------------------------------
    So, the two equations in your question here are both circles, although the last one is imaginary because the sum of two squared quantities (after completing the squares) cannot be negative. --------answer.
    I should add that these are most of the forms you are going to meet: the ones where the axes of symmetry lie parallel to the x or y axes. However not all of the conic sections you will run into will have these kinds of axes of symmetry and they will appear in the general form of:
    Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0

    It is the presence of the xy term that will tell you that you have one of these. You'll be taught how to handle these in your class in due course if you are going to run into them.

    -Dan
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Junior Member
    Joined
    Aug 2007
    Posts
    58
    Quote Originally Posted by ticbol View Post
    I don't know if you have studied yet all those: line, parabola, ellipse, hyperbola, circle. If yes, then you may understand my answer. If not all of them yet, then you will not fully understand my answer.

    Line.
    It is linear or of degree 1. Meaning, the x or the y have exponents of 1 only.
    It is in the form, y = Ax +B. Or, Ax +By +C = 0.

    Parabola.
    It is quadratic, or of degree 2. One of the variables is of degree 1 only, though.
    It is in the expanded form, y = Ax^2 +Bx +C. Or x = Ay^2 +By +C.

    Circle.
    It is quadratic, or of degree 2. Both variables are in degree 2. The coefficients of the two squared variables are equal or the same. It is the sum of the two squared variables, etc.
    In its expanded form, Ax^2 +Ay^2 +Bx +Cy +D = 0
    See that Ax^2 + Ay^2 ?

    Ellipse.
    It is quadratic, or of degree 2. Both variables are in degree 2. The coefficients of the two squared variables are unequal or not the same. It is the sum of the two squared variables, etc.
    In its expanded form, Ax^2 +By^2 +Cx +Dy +E = 0
    See that Ax^2 + By^2 ?

    Hyperbola.
    It is quadratic, or of degree 2. Both variables are in degree 2. The coefficients of the two squared variables may be equal or not equal. It is the subtraction of the two squared variables, etc.
    In its expanded form, Ax^2 -Ay^2 +Bx +Cy +D = 0
    Or, Ax^2 -By^2 +Cx +Dy +E = 0
    See those Ax^2 -Ay^2, or Ax^2 -By^2 ?
    ----Sometimes it has the "xy" term in the expanded form, even if the squared variables as not in there. Meaning, if you see a quadratic equation with an "xy" term, sum or subtraction, the equation is hyperbola.

    -------------------------------
    So, the two equations in your question here are both circles, although the last one is imaginary because the sum of two squared quantities (after completing the squares) cannot be negative. --------answer.

    thanks that helped me a lot
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Classify the graph of the equation
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 7th 2011, 01:27 PM
  2. Where to classify that problem?
    Posted in the Advanced Math Topics Forum
    Replies: 1
    Last Post: November 10th 2011, 12:40 AM
  3. Classify the beam
    Posted in the Geometry Forum
    Replies: 0
    Last Post: September 15th 2010, 08:52 AM
  4. Classify an equation
    Posted in the Pre-Calculus Forum
    Replies: 7
    Last Post: December 9th 2009, 02:53 AM
  5. Classify Equation
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 2nd 2008, 11:59 PM

Search Tags


/mathhelpforum @mathhelpforum