Results 1 to 3 of 3

Thread: finding values....

  1. June 14th 2009, 08:58 PM #1
    dan123
    dan123 is offline
    Junior Member
    Joined
    Apr 2009
    Posts
    44

    finding values....

    2x^2+Cy^2+Dx+Ey+F=0 represents a conic. state the values of C for which each of the following are possible

    a circle

    an ellipse

    a parabola

    a hyperbola
    Follow Math Help Forum on Facebook and Google+
  2. June 14th 2009, 09:07 PM #2
    yeongil
    yeongil is offline
    Super Member
    Joined
    May 2009
    Posts
    527
    The general form of a second-degree quadratic in 2 variables is
    Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0.

    We have to check the expression B^2 - 4AC to determine the type of conic.

    If B^2 - 4AC > 0, then we have a hyperbola.

    If B^2 - 4AC = 0, then we have a parabola.

    If B^2 - 4AC < 0, then we have either a circle or an ellipse. If B = 0 and A = C, then we have a circle. Otherwise, it's an ellipse.

    Now try your problem. B = 0 and A = 2...


    01
    Follow Math Help Forum on Facebook and Google+
  3. June 15th 2009, 04:00 AM #3
    Soroban
    Soroban is offline
    Super Member
    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,242
    Thanks
    370
    Hello, Dan!

    You're expected to know the general forms of the four conics.

    2x^2+Cy^2+Dx+Ey+F\:=\:0 represents a conic.
    State the values of C for which each of the following are possible:

    (a) a circle
    The coefficients of x^2 and y^2 must be equal.
    . . C \:=\:2


    (b) an ellipse
    The coefficients of x^2 and y^2 are unequal, but have the same sign.
    . . C \:>\:0\:\text{ and }\:C \:\neq\: 2


    (c) a parabola
    The equation has x^2 or y^2, but not both.
    . . C \:=\:0


    (d) a hyperbola
    The coefficients of x^2 and y^2 must have opposite signs.
    . . C \:<\:0
    Follow Math Help Forum on Facebook and Google+
« Equation : Ln | 2^x≤ 3^x »

Similar Math Help Forum Discussions

  1. Finding the values of a and b
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: April 18th 2011, 01:46 AM
  2. Finding the values of a and b
    Posted in the Algebra Forum
    Replies: 5
    Last Post: October 1st 2010, 01:01 AM
  3. Finding the values of p and q
    Posted in the Algebra Forum
    Replies: 8
    Last Post: June 1st 2010, 11:00 AM
  4. Finding max min values
    Posted in the Math Software Forum
    Replies: 6
    Last Post: December 8th 2009, 01:18 PM
  5. Finding Values
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 14th 2009, 05:35 PM

Search Tags


/mathhelpforum @mathhelpforum