The lengths of the major and minor axes of the ellipse $4 {(x - 2 y + l)}^{2} + 9 {(2 x + y + 2)}^{2} = 180$ are

3, 2

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9, 8

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6, 4

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10, 5

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Solution

The correct option is C $6, 4$
$y (x - 2 y + l)^{2} + 9 (2 x + y + 2)^{3} = 180$
$\frac{(x - 2 y + l)}{a^{2} = 9} + \frac{(y + 2 x + 2)^{2}}{b^{2} = 4} = 5$
$∴$ length of major axis = $2 a$
$= 2 \times 3 = 6$
and length of major axis = $2 b$
$= 2 \times 2$
$= 4$
Option (C) is correct.

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