Question

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

Focus at (4, 0);  Vertex at (0, 0)

Answer 1

Step 1:

The vertex is  and focus is .

The equation of parabola with vertex , focus and directrix  is .

Here  and directrix is .

Required equation of parabola is .

.

Points of latus rectum can be found by substituting   in .

Find the two points of latus rectum by substituting  in .

.

Points that define latus rectum are .

Step 2:

Graph the parabola and plot the all the points.

Solution:

Latus rectum points are .

Graph of the parabola is