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Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

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Section
BuyFindarrow_forward

Algebra and Trigonometry (MindTap ...

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

55-64 ■ Find the Equation of the Conic Find an equation for the conic section with the given properties.

The parabola with focus F ( 0 , 1 ) and directrix y = 1 .

To determine

To find:

An equation for the parabola with focus F(0,1) and directrix y=1.

Explanation

Given:

The focus and directrix of the parabola are F(0,1) and y=1 respectively.

Approach:

Take a point P(x0,y0) on the parabola, Then the perpendicular distance from 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 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=(x00)2+(y01)2

Let PB be the perpendicular distance between point P(x0,y0) and directrix, y+1=0.

Then

PB=|y0+1|

Equate distances PF and PB, and square both sides

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Chapter 12 Solutions

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