AP EAMCET · Maths · Circle
The set of all points that are at a distance of at least 2 units from \((-3,0)\) is
- A \(\left\{(x, y) \mid x^2+y^2+6 x-7>0\right\}\)
- B \(\left\{(x, y) \mid x^2+y^2+6 x+5 \geq 0\right\}\)
- C \(\left\{(x, y) \mid x^2+y^2+6 x+5 < 0\right\}\)
- D \(\left\{(x, y) \mid x^2+y^2+6 x+7 \leq 0\right\}\)
Answer & Solution
Correct Answer
(B) \(\left\{(x, y) \mid x^2+y^2+6 x+5 \geq 0\right\}\)
Step-by-step Solution
Detailed explanation
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 \((-3,0)\) \(\begin{aligned} & (x+3)^2+(y-0)^2 \geq 2^2 \\ & x^2+9+6 x+y^2 \geq 4 \\ & x^2+y^2+6 x+5 \geq 0\end{aligned}\)
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