Question

Find the set of all points at a distance of at least 2 units from the point \( (-3, 0) \).

• 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. \( \{(x, y) \mid x^2 + y^2 + 6x + 7 \leq 0 \} \)

Hint:

Distance r means inequality of squared distance \( r^2 \). Expand and simplify using standard distance formula.

Answer 1

The Correct Option is B

The distance from \( (-3, 0) \) to a point \( (x, y) \) is: \[ \begin{align} \sqrt{(x + 3)^2 + y^2} \geq 2 \Rightarrow (x + 3)^2 + y^2 \geq 4 \Rightarrow x^2 + 6x + 9 + y^2 \geq 4 \Rightarrow x^2 + y^2 + 6x + 5 \geq 0 \]