Question:
The centre of the ellipse $4x^{2}+24x+9y^{2}-18y+9=0$ is ________.
The centre of the ellipse $4x^{2}+24x+9y^{2}-18y+9=0$ is ________.
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The centre is found by setting the partial derivatives with respect to $x$ and $y$ to zero.
Updated On: Jun 26, 2026
- $(1, 3)$
- $(-1, 3)$
- $(3, 1)$
- $(-3, 1)$
- $(3, 3)$
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The Correct Option is D
Solution and Explanation
Step 1: Concept
Complete the squares for $x$ and $y$ terms.
Step 2: Meaning
$4(x^2+6x+9) + 9(y^2-2y+1) = -9 + 36 + 9$.
$4(x+3)^2 + 9(y-1)^2 = 36$.
Step 3: Analysis
The equation is of the form $\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1$, where $(h, k)$ is the centre.
Step 4: Conclusion
Centre is $(-3, 1)$. Final Answer: (D)
Complete the squares for $x$ and $y$ terms.
Step 2: Meaning
$4(x^2+6x+9) + 9(y^2-2y+1) = -9 + 36 + 9$.
$4(x+3)^2 + 9(y-1)^2 = 36$.
Step 3: Analysis
The equation is of the form $\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1$, where $(h, k)$ is the centre.
Step 4: Conclusion
Centre is $(-3, 1)$. Final Answer: (D)
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