Question

The center of the ellipse \( \frac{(x+1)^{2}}{9} + \frac{(y-2)^{2}}{4} = 1 \) is:

• A. $(1, -2)$
• B. $(-1, 2)$
• C. $(9, 4)$
• D. $(0, 0)$

Hint:

The center is the point that makes the squared terms in the numerator zero.

Answer 1

The Correct Option is B

Step 1: Concept
The standard form $\frac{(x-h)^{2}}{a^{2}} + \frac{(y-k)^{2}}{b^{2}} = 1$ has its center at $(h, k)$.
Step 2: Analysis
Comparing the given equation: $x - h = x + 1 \Rightarrow h = -1$ and $y - k = y - 2 \Rightarrow k = 2$.
Step 3: Conclusion
The center is $(-1, 2)$.
Final Answer: (B)