Question

A parabola is represented by the equation y2 = 5x. Which equation represents the directrix? Y = –20 x = –20 y = Negative five-fourths x = Negative five-fourths

Answer 1

D on edg 2021

Step-by-step explanation:

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Answer 2

`x = - (5)/(4)`

Step-by-step explanation:

Given

`y^2 = 5x`

Required

Determine the directrix

First, we express the equation in form:

`(y - k)^2 = 4p (x - h)`

Where the directrix is:

`x = h - p`

So, we have:

`y^2 = 5x`

Rewrite as:

`(y - 0)^2 = 5(x - 0)`

Multiply the right hand side by 4/4

`(y - 0)^2 = (4)/(4) * 5(x - 0)`

`(y - 0)^2 = 4* (5)/(4) (x - 0)`

By comparison:

`(y - k)^2 = 4p (x - h)` and
`(y - 0)^2 = 4* (5)/(4) (x - 0)`

`k = 0`

`p =(5)/(4)`

`h = 0`

The directrix is calculated as:

`x = h - p`

So:

`x = 0 - (5)/(4)`

`x = - (5)/(4)`