   Chapter 10.1, Problem 45E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

Use the Distance Formula to show that the equation of the parabola with focus F 0 ,   1 and directrix y = - 1 is y = 1 4 x 2 .

To determine

To show:

The equation of the parabola with focus F0, 1 and directrix y=-1 is y=14x2 by using the distance formula.

Explanation

The focus of the parabola is F0, 1.

The directrix of the parabola is y=-1.

Let x, y be any point on the parabola.

We have to find the distance between the point x, y and focus F0, 1.

x1,y1=x, y

x2,y2=0, 1

Formula for distance between two points

d=x2-x12+y2-y12

Substituting the x and y co-ordinates

d=0-x2+1-y2

On solving this,

d=-x2+1-y2

d=x2+1-y2

Now, we have to find the distance between the point x, y and directrix y=-1.

d=y--1

d=y+1

Now, we have to equate both the distances

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