Integrate the function $ f(x, y, z) = x^2 + y^2$ on the region $R$ bounded by $\frac{x^2}{4}+y^2=1$ , $z=0$ and a cone with vertex in $(0,0,5)$ and has for base the same elipse.
My principal struggle here is finding an equation for the cone, also I am hinted to use the transformation
$$x = 2 \left( 1-\frac{w}{5} \right) r \cos(\theta), \quad y = \left( 1-\frac{w}{5} \right) r \sin(\theta), \quad z = w $$