# Bivariate Contour Ellipse Area

#### m1chael

##### New Member
I have found a research paper, where there is need to calculate the area of a bivariate contour ellipse. I am familiar with drawing a confidence ellipse, so my concern is about the formulas provided in this publication.
As it is mentioned the bivariate contour ellipse area is calculated with the following formula:

$area=2k\pi\sigma_{x}\sigma_{y}\sqrt{1-\rho^2}$ (1)
where $\rho$ is the product moment correlation coefficient and $\sigma_{x},\sigma_{y}$ are the standard deviations of the two variables.

It also states that k can be calculated through probability equation
$P=1-e^{^{-k}}$ (2)

I need help to understand which probability function is equation (2) and how we get as outcome for the area calculation equation (1)