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Chapter 10: Q 20. (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 at0,2and its vertex at0,0.

Short Answer

Expert verified

The equation of a parabola will be

x2=8y.

The two points are 4,2and -4,2.

The graph of an equation will be

Step by step solution

01

Step 1. Given Information.

The given vertex is at 0,0and its focus is at0,2.

02

Step 2. Observation.

Observe the vertex and focus points , the x-coordinate are same and on y-axis. Thus, the parabola is vertical.

03

Step 3. Equation of a parabola.

The distance from the vertex 0,0to the focus 0,2is a=2.

The equation of the parabola is

x2=4ay.

role="math" localid="1646650258552" a=2鈬�x2=8y.

04

Step 4. Calculation of a Latus rectum.

We need to find the two points that determine the latus rectum by letting y=2. Then,

x2=8yx2=82x2=16x=卤4

The points 4,2and -4,2determine the latus rectum.

05

Step 5. Graphing utility.

The graph will be

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Most popular questions from this chapter

Searchlight - A searchlight is shaped like a paraboloid of

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Hyperbolic Mirrors Hyperbolas have interesting reflective properties that make them useful for lenses and mirrors. For example, if a ray of light strikes a convex hyperbolic mirror on a line that would (theoretically) pass through its rear focus, it is reflected through the front focus. This property, and that of the parabola, were used to develop the Cassegrain telescope in 1672. The focus of the parabolic mirror and the rear focus of the hyperbolic mirror are the same point. The rays are collected by the parabolic mirror, reflected toward the (common) focus, and thus are reflected by the hyperbolic mirror through the opening to its front focus, where the eyepiece is located. If the equation of the hyperbola is y29-x216=1 and the focal length (distance from the vertex to the focus) of the parabola is 6, find the equation of the parabola.

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