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

Answer:

$x = - \frac{5}{4}$

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

$(y - 0)^2 = \frac{4}{4} * 5(x - 0)$

$(y - 0)^2 = 4* \frac{5}{4} (x - 0)$

By comparison:

$(y - k)^2 = 4p (x - h)$ and $(y - 0)^2 = 4* \frac{5}{4} (x - 0)$

$k = 0$

$p =\frac{5}{4}$

$h = 0$

The directrix is calculated as:

$x = h - p$

So:

$x = 0 - \frac{5}{4}$

$x = - \frac{5}{4}$

Answer 2

Answer:

D on edg 2021

Explanation:

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