WeBWorK Standalone Renderer

(a) Find a linear change of coordinates that takes the unit circle $u^2 + v^2 = 1$ in the $uv$ -plane to the ellipse $\displaystyle 3 x^2 + 36 y^2 = 64$ in the $xy$ -plane.

$x = x(u,v) =$
$y = y(u,v) =$

(b) Find the absolute value of the determinant of the Jacobian for this change of coordinates.

$\displaystyle \left| \frac{\partial(x,y)}{\partial(u,v)} \right| = \bigg| \mathrm{det}$

$\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$			$\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$

$\bigg| =$

(c) Use your answer to part (b) to find the area enclosed by the ellipse $3 x^2 + 36 y^2 = 64$ .

Area =

You can earn partial credit on this problem.