## Thomas' Calculus 13th Edition

Published by Pearson

# Appendices - Section A.3 - Lines, Circles, and Parabolas - Exercises A.3 - Page AP-17: 4

#### Answer

The interior of the circle of radius $r=\sqrt{3}$, centered at the origin, including the circle itself.

#### Work Step by Step

Equation (1) in the text, $(x-h)^{2}+(y-k)^{2}=r^{2}$ is the standard equation for a circle of radius $r,$ centered at $(h,k)$, $x^{2}+y^{2}=3$ is a circle of radius $r=\sqrt{3}$, centered at the origin. This circle divides the plane into two regions: the interior and exterior of the circle. Testing coordinates of the origin, $0^{2}+0^{2}\leq 3,$ we see that the origin belongs to the solution set. The inequality sign $\leq$ indicates that the border line (the circle) is included in the solution set. The region represented by the inequality is the interior of the circle of radius $r=\sqrt{3}$, centered at the origin, including the circle itself.

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