we know that
Any point (x,y) on the parabola is equidistant from the focus and the directrix
Therefore,
focus (0,4) and directrix of y=2
√[(x−0)²+(y−4)²]=y−(2)
√[x²+(y-4)²]=y-2
x²+(y-4)²=(y-2)²
x²+y²-8y+16=y²-4y+4
x²=4y-12-----> 4y=x²+12----->y= (x²/4)+3
the answer is
y= (x²/4)+3
