   Chapter 10, Problem 50RE

Chapter
Section
Textbook Problem

Find an equation of the parabola with focus (2, 1) and directrix x = −4.

To determine

To find: The equation of the parabola with focus (2,1) and directrix x=4 .

Explanation

Given:

The focus of the parabola is at (x1,y1)=(2,1) .

The directrix is at x=4 .

Calculation:

The distance of the point (x,y) from the directrix line x=4 is |x+4| .

|x+4| (1)

The distance of the point (x,y) from the focus (2,1) is (xx1)2+(yy1)2 .

Substitute (x1,y1)=(2,1) in the above equation.

(x2)2+(y1)2 (2)

Equate the terms in equation (1) and (2)

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