Write the equation in vertex form and then find the vertex, focus, and directrix of a parabola with equation x=y^2+18y-2

Part 1) The vertex is the point (-83,-9)

Part 2) The focus is the point (-82.75,-9)

Part 3) The directrix is

Step-by-step explanation:

step 1

Find the vertex

we know that

The equation of a horizontal parabola in the standard form is equal to

where

p≠ 0.

(h,k) is the vertex

(h + p, k) is the focus

x=h-p is the directrix

In this problem we have

Convert to standard form

so

This is a horizontal parabola open to the right

(h,k) is the point (-83,-9)

so

The vertex is the point (-83,-9)

step 2

we have

Find the value of p

Find the focus

(h + p, k) is the focus

substitute

(-83+1/4,-9)

The focus is the point (-82.75,-9)

step 3

Find the directrix

The directrix of a horizontal parabola is

substitute