Question

Find the coordinates of the focus and equation of the directrix for the parabola given by

y2 = −4x.

The general formula for this parabola is y2 = 4px.

Therefore, the value of p is _____

The coordinates of the focus are ______

The equation of the directrix is ______

Answer 1

Answer: P is -1

Focus is (-1,0)

Directrix is X= 1

Answer 2

The answers to your three problem question are shown

1) the value of p is

p = -1

2) The coordinates of the focus are

Focus = (-1,0)

3) The equation of the directrix is

Directrix

x = 1

Explanation:

The general equation for this parabola is

y^2 = 4px

Problem 1

Find the value of p.

We are told that the equation of the problem is

y^2 = -4x

And the general formula is

y^2 = 4px

From there, we can deduce that

p = -1, because

y^2 = 4(-1)x = -4x

This means that p = -1

Problem 2

Find the focus

To find the focus we can see the equations attached below for the focus, vertex and directrix.

In these case, the equations still apply, even though the variable is inverted, we just need to adjust it

y^2 = -4x =>

x = (-1/4)*y^2

x = a*y^2 + b*y +c

Focus

((4ac -b^2 + 1)/4a, -b/2a)

But, b = 0 and c = 0

=>

(1/4a,0) = (1/4(-1/4),0) = (-1,0)

Focus = (-1,0)

Problem 3

Find the directrix

The equation is

x = c - (b^2 + 1).4a

But, b = 0 and c = 0

x = -4*a

x = -4* (-1/4) = 1

x = 1

Directrix

x = 1