Question

The equation of a parabola is `x=-4(y-1)^2`. What is the equation of the directrix?

Answer 1

The equation of directrix is `x=1/16`

Explanation:

`x= -4(y-1)^2 or (y-1)^2= -1/4(x-0) or (y-1)^2= -4*1/16(x-0)`

Comparing with standard equation `(y-k)^2 = -4a(x-h)` we find here `h=0,k=1, a= -1/16`.

The parabola opens left with vertex as `(h,k) or (0,1)` focus at `(-a,0) or (-1/16,0)`

The equation of directrix is `x=a or x=1/16`
graph{x=-4(y-1)^2 [-10, 10, -5, 5]}