Centre of the ellipse $4 (x - 2 y + 1)^{2} + 9 (2 x + y + 2)^{2} = 5$ is

(- 2, 2)

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(1, 5)

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(- 5, 2)

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(- 1, 0)

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Solution

The correct option is D $(- 1, 0)$
Centre is point of intersection of lines
$x - 2 y + 1 = 0$ and $2 x + y + 2 = 0$
Solving both equations
$\Rightarrow y = 0$
$x + 1 = 0 \Rightarrow x = - 1$

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