Parabola focus is at  and vertex is .

Since the -coordinates are equal, the parabola is horizontal.

Standard form of horizontal parabola is .

Where is vertex.

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

Directrix is  and focus at .

Focus .

.

Substitute and in .

.

The directrix 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 :

.