Question

If R is the region inside (x^(2))/(4)+(y^(2))/(36)=1 determine the region we would get applying the tranformation x=2u,y=4v to R.

Answer 1

By substituting the given values of x and y into the equation, the region obtained by applying the transformation x=2u, y=4v is u^2+v^2=1, which represents a circle.

Step-by-step explanation:

To determine the region obtained by applying the transformation x=2u, y=4v to the region inside the equation (x^2)/4+(y^2)/36=1, we need to substitute the given values of x and y into the equation.

Substituting x=2u and y=4v, we get ((2u)^2)/4+((4v)^2)/36=1. Simplifying this equation, we get u^2+v^2=1.

Therefore, the new region we obtain by applying the transformation is the equation u^2+v^2=1, which represents a circle.