Question

The largest distance from (-3, 2) to the circle $x^{2} + y^{2} - 2x + 2y + 1 = 0$

• A. 8
• B. 4
• C. 18
• D. 6

Hint:

Max distance = $PC + R$; Min distance = $|PC - R|$.

Answer 1

The Correct Option is A

Step 1: Concept
The maximum distance from a point $P$ to a circle with center $C$ and radius $R$ is $PC + R$.

Step 2: Meaning
For the circle $x^{2} + y^{2} - 2x + 2y + 1 = 0$, center $C = (1, -1)$ and radius $R = \sqrt{1^{2} + (-1)^{2} - 1} = 1$.

Step 3: Analysis
Distance $PC = \sqrt{(-3-1)^{2} + (2-(-1))^{2}} = \sqrt{(-4)^{2} + 3^{2}} = \sqrt{16 + 9} = 5$.

Step 4: Conclusion
Largest distance = $PC + R = 5 + 1 = 6$. Final Answer: (A)