A consumer has the utility function $u(x_1,x_2)=(x_1^a+x_2^a)^{1/a}$ where 0\neq a<1. Her expenditure must satisfy $p_1x_1+p_2x_2=I$, where $p_i$ is the price of a good i, and I is her income. Find the optimum consumption bundle. Describe Engel's curve for these preferences. Compute the own price elasticity and cross-price elasticity for both goods.
Attempt:
I found the optimum consumption bundle by forming the Lagrangian. The optimum consumption bundle is:
$x_1=\frac{I}{p_1(1+(\frac{p_1}{p_2})^{\frac{a}{1-a}})}\;\;\;\;\;\;\;\;\;x_2=\frac{I}{p_2(1+(\frac{p_2}{p_1})^{\frac{a}{1-a}})}$
Now I need to describe the Engel's curve for these preferences. What should I do?
I also have little idea how to compute the own price elasticity and cross-price elasticity of both goods.