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

The set of all points that are at a distance of at least 2 units from $(-3,0)$ is
  1. $\left\{(x, y) \mid x^2+y^2+6 x-7>0\right\}$
  2. $\left\{(x, y) \mid x^2+y^2+6 x+5 \geq 0\right\}$
  3. $\left\{(x, y) \mid x^2+y^2+6 x+5 < 0\right\}$
  4. $\left\{(x, y) \mid x^2+y^2+6 x+7 \leq 0\right\}$

Solution

Consider the point to be $(x, y)$ Now, the collection of such points will be all points on or outside a circle of radius 2 units whose centre is at $(-3,0)$ $\begin{aligned} & (x+3)^2+(y-0)^2 \geq 2^2 \\ & x^2+9+6 x+y^2 \geq 4 \\ & x^2+y^2+6 x+5 \geq 0\end{aligned}$

Asked in: AP EAMCET 2022 (05 Jul Shift 2)

Practice more Circle questions on Aicharya