Answer:
f(x) = one eigth (x-2)^2 - 1
Step-by-step explanation:
We have. focus = (2,1) and directrix y = -3.
Let (x,y) be any point on the curve.
First, we will find the distance between (x,y) and the focus (2,1).
i.e. distance = 
Now, we will find the distance between (x,y) and directrix y = -3.
i.e. distance = | y - (-3) | = | y + 3 |
To find the quadratic function, we will equate both the distances and simplify the equation.
i.e.
= | y + 3 |
Squaring both sides, we get,

i.e. 
i.e. 
i.e. 
The option f(x) = one eigth (x-2)^2 - 1 will give the y obtained above after simplifying.