2014 SRJC Promo Q4

A curve undergoes, in succession, the following transformations:

A: A reflection in the \(y\)-axis

B: A translation of \(3\) units in the negative \(y\)-direction

C: A translation of \(4\) units in the positive \(x\)-direction

D: A scaling parallel to the \(x\)-axis by a factor of \(2\)

The equation of the resulting curve is \(y=\sqrt{1-\frac{{{x}^{2}}}{4}}\).

Determine the equation of the original curve before the transformations were carried out.[5]