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Chapter 10: Q 22. (page 643)

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

Focus is at-4,0and vertex is at0,0.

Short Answer

Expert verified

The equation of a parabola is

y2=-16x.

The latus rectum points are-4,8and-4,-8.

Step by step solution

01

Step 1. Given Information.

The given points of an equation are :

focus-4,0and vertex0,0.

02

Step 2. Equation of a parabola.

The distance from the vertex 0,0and its focus -4,0is a=-4.

The equation of a parabola be :

y2=4axy2=-16x.

03

Step 3. Calculation of a latus rectum.

The two points that determine the latus rectum by letting x=-4. Then,

y2=-16xy2=-16-4y2=64y=卤8.

The points are-4,8and-4,-8.

04

Step 4. Graphing utility.

The graph of a parabola be:

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