(B) Let the point be $(x, y)$.The set of points at a distance of at least $2$ units from the center $(-3, 0)$ represents the region on or outside the

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$\{(x, y) \mid x^2+y^2+6x+5 \geq 0\}$

(B) Let the point be $(x, y)$.The set of points at a distance of at least $2$ units from the center $(-3, 0)$ represents the region on or outside the circle with radius $r = 2$.The distance formula gives: $\sqrt{(x - (-3))^2 + (y - 0)^2} \geq 2$.Squaring both sides: $(x + 3)^2 + y^2 \geq 2^2$.Expanding the expression: $x^2 + 6x + 9 + y^2 \geq 4$.Rearranging the terms: $x^2 + y^2 + 6x + 5 \geq 0$.

Class 11 Mathematics 10-1.Circle and System of Circles Locus Related Problem

Medium

The set of all points that are at a distance of at least $2$ units from $(-3, 0)$ is

AP EAMCET 2022 All AP EAMCET

A
$\{(x, y) \mid x^2+y^2+6x-7 > 0\}$
B
$\{(x, y) \mid x^2+y^2+6x+5 \geq 0\}$
C
$\{(x, y) \mid x^2+y^2+6x+5 < 0\}$
D
$\{(x, y) \mid x^2+y^2+6x+7 \leq 0\}$

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