Question

What equation represents a parabola with a focus of (0,4) and a directrix of y=2

Answer 1

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