Identify the directrix of y - 4 = (1/4)(x - 2)^2.?

Question

Identify the directrix of y - 4 = (1/4)(x - 2)^2.?

Answer 1

Put

X = x -2,

Y = y - 4.  Then

4Y = X^2

This is a standard Parabola with a = 1.

Focus is (Y + 1) with X = 0 {Apex is at X =0, Y = 0}

Hence, Directrix is at -a distance

X = -1.

Putting back original variables

Directrix is

x - 2 = -1

=> x = 1    {focus (2, 5) and apex is (2, 4) in terms of (x, y)}