Thread: How do you tell a cricle by the formula?

1. 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?

2. Originally Posted by dankelly07
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 $\displaystyle e^{-x^2-y^2} = a$ where $\displaystyle a$ is a constant then you would do the following:

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

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

It will obviously be a circle if $\displaystyle 0 < a < 1$.

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