Question

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

 Directrix the line y = - 1/2;   Vertex at (0, 0)

Answer 1

Step 1:

Vertex is  and directrix line is .

The standard form of the equation of the parabola with vertex  and directrix is  is

.

Here focus is .

Compare the vertex and directrix with the standard form.

.

Focus is .

Substitute  in .

 

The equation of parabola is .

Points of the latus rectum of the above standard form can be determined by substituting  in

.

Find points of latus rectum by substituting  in .

.

Points that define latus rectum are  and.

Step 2:

Graph the parabola .

Plot the all required points.

Solution:

Latus rectum points are  and.

The equation of parabola is .