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Chapter 10: Q. 32 (page 643)

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

Vertex at 3,0; focus at3,-2

Short Answer

Expert verified

The equation of parabola is x-32=8y+2and the graph of the equation shown below. The two points of latus rectum are3,2,3,-2.

Step by step solution

01

Step 1. Given information .

Consider the given vertex and focus points .

02

Step 2. Formula used .

The formula used to find the equation of parabola is x-h2=4ay-k.

Substitute the values in the given formula .

Here h,k=3,0and x,y=3-2

x-h2=4ay-kx-32=4路2y+2x-32=8y+2

Since the symmetry is at x axis then x=3.

Substitute the value in standard form of parabola we get the the two points that define latus rectum.

Further simplify .

x2=4aywhere a=-98,y=-2we get points3,23,-2.

03

Step 3.  Plot the graph .

The graph of the equation x-32=8y+2of parabola is shown below.

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