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Zeroes of a Polynomial

Factorise 4y...

Question

Factorise
$4 y^{2} + 9 x^{2} - 40 y - 54 x + 145 = 0$ .

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Solution

$4 y^{2} + 9 x^{2} - 40 y - 54 x + 145 = 0$
$4 (y^{2} - 10 y + 25) + 9 (x^{2} - 6 x + 9) = 36$
$9 (x - 3)^{2} + 4 (y - 5)^{2} = 36$
$\frac{(x - 3)^{2}}{4} + \frac{(y - 5)^{2}}{9} = 1$

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