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how to quickly judge which is an ellips hyperbola or parabola

how to quickly judge which is an ellips hyperbola or parabola


1 Answers

25768 Points
3 years ago
  • Circle. When and are both squared and the coefficients on them are the same — including the sign.

    For example, take a look at 3x2 – 12x + 3y2= 2. Notice that the x2 and y2 have the same coefficient (positive 3). That info is all you need to recognize that you’re working with a circle.

  • Parabola. When either or y is squared — not both.

    The equations y = x2 – 4 and x = 2y2 – 3y + 10 are both parabolas. In the first equation, you see an x2 but no y2, and in the second equation, you see a y2 but no x2. Nothing else matters — signs and coefficients change the physical appearance of the parabola (which way it opens or how fat it is) but don’t change the fact that it’s a parabola.

  • Ellipse. When and y are both squared and the coefficients are positive but different.

    The equation 3x2 – 9x + 2y2 + 10y – 6 = 0 is one example of an ellipse. The coefficients of x2 and y2 are different, but both are positive.

  • Hyperbola. When and are both squared, and exactly one of the coefficients is negative and exactly one of the coefficients is positive.

    The equation 4y2 – 10y – 3x2 = 12 is an example of a hyperbola. This time, the coefficients of x2 and y2 are different, but exactly one of them is negative and one is positive, which is a requirement for the equation to be the graph of a hyperbola

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