1. For Real λ>0, λ=/=1, consider the point x∈ R^k that satisfy.
||x-a|| = λ||x-b||
Show that these points lie on a sphere. Part of this is to find the center and radius of
this sphere in terms of a, b and λ. What if λ = 1?
2. Find an orthogonal basis for the space P2 of quadratic polynomials with the inner
product
hf, gi = f(−1)g(−1) + f(0)g(0) + f(1)g(1)
