Convex set, quadratic form I'm trying to answer a question concerning convex sets
"Does the following constraint system define a convex set?
$x^T Qx ≤ 1$
$a^T x = 0$
Here, Q is a symmetric and positive definite matrix and a is a vector.
Give a graphical motivation of your answer."
But I can't figure it out.
I'm guessing that $a^T x = 0$ is a line (at least in 2- or 3-dim). But have no idea of how the quadratic form would look like and how it is relevant that it is symmetrical. That it is positive definite must mean that $x^T Qx > 0$, but I don't see how that is relevant.
Any hints?

Yes. The first equation defines a convex set. The second constraint also defines a convex set. An intersection of convex sets is convex.
