Question

The equation of a circle whose Centre is $(-3, 2)$ and area is $176$ units is:

• A. $x^2 + y^2 + 6x - 4y - 36 = 0$
• B. $x^2 + y^2 + 6x - 4y - 43 = 0$
• C. $x^2 + y^2 - 6x + 4y - 36 = 0$
• D. $x^2 + y^2 - 6x + 4y - 43 = 0$

Hint:

Center $(h, k)$ means the equation starts with $x^2 + y^2 - 2hx - 2ky$. For $(-3, 2)$, it's $+6x - 4y$.

Answer 1

The Correct Option is B

Step 1: Concept
Use the area to find the radius $r$ ($\text{Area} = \pi r^2$) and use the standard form $(x-h)^2 + (y-k)^2 = r^2$.

Step 2: Meaning
Given Area $\approx 176 \implies \frac{22}{7} r^2 = 176 \implies r^2 = 176 \times \frac{7}{22} = 56$.

Step 3: Analysis
Equation: $(x - (-3))^2 + (y - 2)^2 = 56 \implies (x+3)^2 + (y-2)^2 = 56$.

Step 4: Conclusion
$x^2 + 6x + 9 + y^2 - 4y + 4 = 56 \implies x^2 + y^2 + 6x - 4y - 43 = 0$.
Final Answer: (B)