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Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

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Chapter
Section
BuyFindarrow_forward

Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

Find an equation for the parabola with focus ( 2 , 4 ) and directrix the x -axis.

To determine

To find:

An equation for the parabola with focus (2,4) and directrix the x-axis.

Explanation

Given:

The focus and directrix of the parabola are (2,4) and x-axis respectively.

Approach:

Take a point P(x0,y0) on the parabola, Then the perpendicular distance from a point P to the directrix is equal to the distance between point P and focus because the eccentricity is equal to one in case of the parabola.

Calculation:

Consider an arbitrary point P(x0,y0) on the parabola. Its distance from the focus F(2,4) is given as follows,

PF=(x02)2+(y04)2

Let PB be the perpendicular distance between point P(x0,y0) and directrix, y=0.

Then

PB=|y00|=|y0|

Equate distances PF and PB, and square both sides

(x02)2+(

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Chapter 12 Solutions

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