Question

Find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation.

Focus at (- 2, 0);   directrix the line x = 2

Answer 1

Step 1:

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 .

Step 2:

Focus =

Directrix

Add the equations (1) and (2).

Vertex of parabola is .

Step 3:

Find the value of .

Substitute in equation (1).

Substitute the values and in standard form.

The parabola equation is .

Step 4:

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.

.

Comments

Solution:

The parabola equation is .

The two points that define latus rectum are

Graph of :

.