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Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

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Section
BuyFindarrow_forward

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 ,   2 and directrix y = - 2 is y = 1 8 x 2 .

To determine

To show:

The equation of the parabola with focus F0, 2 and directrix y=-2 is y=18x2 by using the distance formula.

Explanation

The focus of the parabola is F0, 2.

The directrix of the parabola is y=-2.

Let x, y be any point on the parabola.

We have to find the distance between the point x, y and focus F0, 2.

x1,y1=x, y

x2,y2=0, 2

Formula for distance between two points

d=x2-x12+y2-y12

Substituting the x and y co-ordinates

d=0-x2+2-y2

On solving this,

d=-x2+2-y2

d=x2+2-y2

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

d=y--2

d=y+2

Now, we have to equate both the distances

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