Parabola focus at  and directrix is 

Since the directrix is , then the parabola is horizontal.

Standard form of horizontal parabola is .

Where is vertex.

If then the parabola opens to the left and parabola opens to the right.

Directrix is  and focus at .

Focus  = 

.

Directrix 

.

.

Substitute in .

.

Vertex of parabola is .

Find the value of .

Substitute  in .

.

Substitute  and  in standard form.

.

The parabola equation is .

Latus rectum is the line segment of a parabola perpendicular to axis which has both ends on the curve.

Obtain the points define the latus rectum, let 

Then 

The two points that define latus rectum are 

Graph:

Draw the coordinate plane.

Plot the vertex, focus, and the two points 

Draw the directrix line.

Connect the plotted points with smooth curve.

The parabola equation is .

The two points that define latus rectum are 

Graph of :

.