If the shortest distance of the point A(0, a) from the parabola $y=x^2$ is $\frac{\sqrt{4c-1}}{2}$, then : A. $y=\frac{2a-1}{2}$ B. $a=2c$ C. Point A is (0, c) D. Point A is (0, 2c) E, $y=\frac{2c-1}{2}$ Choose the correct answer from the options given below :

A, B Only A, D, E Only A, C, E Only A, E Only

A, C, E Only