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Math Help - How do you tell a cricle by the formula?

  1. #1
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    How do you tell a cricle by the formula?

    I confused about how to tell what shape something will be by its formula.
    for example..

    I know that x^2+y^2=1 is a circle
    and
    sqrt(x^2+y^2)=1 is a semicircle

    but how do you know what a shape like
    exp{-x^2-y^2) would be..?
    Also are there other types of formulas which include the circle formula, that are common as integration problems?
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  2. #2
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    Quote Originally Posted by dankelly07 View Post
    I confused about how to tell what shape something will be by its formula.
    for example..

    I know that x^2+y^2=1 is a circle
    and
    sqrt(x^2+y^2)=1 is a semicircle

    but how do you know what a shape like
    exp{-x^2-y^2) would be..? Mr F says: This defines nothing because there is no = in it.

    Also are there other types of formulas which include the circle formula, that are common as integration problems?
    If your intention is something like e^{-x^2-y^2} = a where a is a constant then you would do the following:

    e^{-x^2-y^2} = a \Rightarrow -x^2 - y^2 = \ln a \Rightarrow x^2 + y^2 = - \ln a.

    This will have no solution if a > 1 (why?) or a \leq 0 (why?).

    It will obviously be a circle if 0 < a < 1.

    If a = 1 it defines the point (0, 0).
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