pre-calculus

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How do i know if a conic section is a circle, ellipse, hyperbola, or parabola? based on it's equation such as 4x^2 - y^2 + 24x + 4y + 28 = 0

  • pre-calculus -

    General equation:
    ax^2 + by^2 + cx + dy + e = 0

    1) if a = b ---> circle
    2) if both a and b are positive, but different, ---> ellipse
    3) if a is positive and b is negative, ----> hyperbola
    4) if either a or b, but not both, are zero ----> parabola
    5) if both a and b are zero ---> straight line

    so yours is a hyperbola

  • pre-calculus -

    Find the transformed equation of the hyperbola xy = 4 when rotated 45?

  • pre-calculus -

    Thanks reiny. This helped a lot.

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