Mark the focus of the parabola you are going to create at f(6, 4). draw a horizontal line that is 6 units below the focus. this line will be the directrix of your parabola. what is the equation of the line?

(You don't need a picture to find the equation.  It's all algebra)

The equation is, depending upon the form you're looking for:

or

Step-by-step explanation:

When you plot the focus and draw in the directrix, you see that the focus is above the directrix.  That means that, since a parabola "hugs" the focus, this parabola opens upwards and is a "y = ax^2" type.  By nature, the vertex is exactly halfway between the focus and the directrix on the same x-coordinate as the focus.  So the coordinates of the vertex, (h, k), are (6, 1).  The p value is the distance between the vertex and either the focus or the directrix (they're the same distance) so p = 3.  The standard form of the parabola we are looking for is:

Filling in, we have, before simplification:

and

If we expand the left side and collect like terms we will get the standard version, which is

It depends upon whether you need one form or the other.  They're the same equation in different forms.

The equation of the line is y = -2,

Step-by-step explanation:

In the coordinate plane (x, y) represents the position of a point,

Where, x shows the location towards x-axis,

While, y shows the location towards y-axis,

Given,

The focus of the parabola is F(6, 4),

That is, the focus will be located 6 unit right from the (0,0),

And, 4 unit up from (6, 0),

Let the equation of directrix,

y = mx + c

Also, directrix is 6 unit below the focus,

Thus the coordinates of a point on the line are (6, -2),

Also, the line is horizontal,

⇒ m = 0 ( slope about x -axis )

Hence, the equation of directrix,

step-by-step explanation:

in which figure is point g a centroid