Explanation Let S be the square centered at the origin and has vertices ( ± a , ± a ) . Note that this square is symmetric about the x -axis, the y -axis and the origin. Thus to describe the region described by the set of points equidistant from the origin it is enough to describe the region in first quadrant as similar logic will follow for rest of the parts. Consider the square S as shown below in Figure 1. First consider any point in a triangle formed by the points ( 0 , 0 ) , ( a , 0 ) and ( a , a ) . Take any point P ( x , y ) that lies inside the triangle and P is equidistant from the square and the origin. The distance of the point P from the origin is x 2 + y 2 . Observe that the point P is closer to the side of the square which is a part of the line x = a than any other side of the square. The perpendicular distance of the point P from the line x = a is a − x . As the point P is equidistant from the square and the origin it satisfies the following condition. x 2 + y 2 = ( a − x ) x 2 + y 2 = a 2 − 2 a x + x 2 y 2 = a 2 − 2 a x The equation y 2 = a 2 − 2 a x describes a parabola opening to the left side. Thus conclude that the point P lies on that parabola as ( x , y ) satisfies the condition. Therefore, any point which lies inside the triangle will lie on the same parabola. Use similar logic for the triangle formed by the points ( 0 , 0 ) , ( 0 , a ) and ( a , a )

Calculus: Early Transcendentals (2nd Edition)

2nd Edition

ISBN: 9780321947345

Author: William L. Briggs, Lyle Cochran, Bernard Gillett

Publisher: PEARSON

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Chapter 10, Problem 66RE

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To describe: The region formed by the set of points which are equidistant from a square centered at origin with vertices (±a,±a) and sketch the region.

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Chapter 10, Problem 65RE

Chapter 10, Problem 67RE

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Calculus: Early Transcendentals (2nd Edition)

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The region formed by the set of points which are equidistant from a square centered at origin with vertices ( ± a , ± a ) and sketch the region.

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To describe: The region formed by the set of points which are equidistant from a square centered at origin with vertices (±a,±a) and sketch the region.

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