I'm given (X,Y) ~ standard bivariate normal (p) -(assume this is the greek letter ro).

I'm asked to find the P(XY>0) as functions of p and other values as indicated.

I know by definition, two random variables X and Y are said to be bivariate normal if and only if aX+bY has a normal distribution. Though, I'm not certain I'm able to satisfy this axiom. Is the product of two normal distributions univariate normal? How should I approach this question?