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Q. 27

Found in: Page 772


Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861

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Short Answer

Use Cartesian coordinates to express the equations for the parabolas determined by the conditions specified in Exercises 22–31.

directrix y=y0, focus x1,y1, where y0y1

The equation is y=12·x-x12y1-y0+y0+y12.

See the step by step solution

Step by Step Solution

Step 1. Given information.

The given values are,

directrix y=y0, focus x1,y1, where y0y1

Step 2. Distance formula.

Let(x,y) be any point on the parabola.

Let (x1,y1) be the focus.

Therefore, by distance formula,

Distance =x1-x2+y1-y2 since x1=x,y1=y,x2=x1,y2=y1 Now the distance between the point and the directrix is y-y0. Therefore,x1-x2+y1-y2=y-y0

Step 3. Final answer.

On simplifying the equation,


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