Solve $9 x^{2} + 4 y^{2} - 36 x + 8 y + 4 = 0$

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Solution

Solution :- given
$\Rightarrow 9 x^{2} + 4 y^{2} - 36 x + 8 y + 4 = 0$

$\Rightarrow 9 x^{2} - 36 x + 36 + 4 y^{2} + 8 y - 32 = 0$

$\Rightarrow 9 (x^{2} - 4 x + 4) + 4 (y^{2} + 2 y - 8) = 0$

$\Rightarrow 9 [(x)^{2} - 2.2 x + 2^{2}] + 4 [y^{2} + 4 y - 2 y - 8] = 0$

$\Rightarrow 9 [x - 2]^{2} + 4 [y (y + 4) - 2 (y + 4)] = 0$

$\Rightarrow 9 [x - 2]^{2} + 4 (y + 4) (y - 2) = 0$

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