Use the parametric equations of an ellipse, x = a cos θ, y = b sin θ, 0 ≤ θ ≤ 2π, to find the area that it encloses.

x = a cos θ

y = b sin θ

0 ≤ θ ≤ 2π

The area encloses

So, Area of encloses ellipse = πab

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The area of the ellipse is

Parameterize by

with and . The Jacobian for this transformation is

with determinant . Then the integral is equivalent to

$650 per month plus utilities

step-by-step explanation:

just based on the info you gave, it would seem more cost effective to rent at $650 per month plus utilities.   if utilities are, in fact, $150 per month, your monthly living costs would be $800 as opposed to the other option of $825.