Question:
Find the set of all points at a distance of at least 2 units from the point \( (-3, 0) \).
Find the set of all points at a distance of at least 2 units from the point \( (-3, 0) \).
Show Hint
Distance r means inequality of squared distance \( r^2 \). Expand and simplify using standard distance formula.
Updated On: May 17, 2025
- \( \{(x, y) \mid x^2 + y^2 + 6x - 7>0 \} \)
- \( \{(x, y) \mid x^2 + y^2 + 6x + 5 \geq 0 \} \)
- \( \{(x, y) \mid x^2 + y^2 + 6x + 5<0 \} \)
- \( \{(x, y) \mid x^2 + y^2 + 6x + 7 \leq 0 \} \)
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The Correct Option is B
Solution and Explanation
The distance from \( (-3, 0) \) to a point \( (x, y) \) is:
\[
\begin{align}
\sqrt{(x + 3)^2 + y^2} \geq 2
\Rightarrow (x + 3)^2 + y^2 \geq 4
\Rightarrow x^2 + 6x + 9 + y^2 \geq 4
\Rightarrow x^2 + y^2 + 6x + 5 \geq 0
\]
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