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Chapter 10: Q 25. (page 643)

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

The directix of a liney=-12and the vertex is at0,0.

Short Answer

Expert verified

The equation of a parabola is x2=2y. The two points of a parabola are -1,12and 1,12.The graph of an equation be :

Step by step solution

01

Step 1. Given Information.

The given vertex is at0,0and the line of directix isy=-12.

02

Step 2. Equation of a parabola.

A parabola whose vertex is at 0,0and whose directix is the horizontal line y=-12. The focus of a parabola is0,12. The equation of the parabola is of the form as

x2=4ayx2=2y

Here,a=12.

03

Step 3. Latus Rectum.

The two points that determines the Latus rectum by letting y=12. Then,

x2=2yx2=212x2=1x=卤1.

The points are1,12and-1,12.

04

Step 4. Graphing utility.

The graph of a parabola is

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