FERMAT 2021 Problem 24

A pair of real numbers (a, b) with a^{2}+b^{2} \leq \frac{1}{4} is chosen at random. If p is the probability that the curves with equations y=a x^{2}+2 b x-a and y=x^{2} intersect, then 100 p is closest to

Answer Choices
A. 65
B. 69
C. 53
D. 57
E. 61