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Properties of Inequalities

Trace the fol...

Question

Trace the following central conics.
$4 x^{2} + 27 x y + 35 y^{2} - 14 x - 31 y - 6 = 0 .$

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Solution

Trace the conic
$4 x^{2} + 27 x y + 35 y^{2} - 14 x - 31 y - 6 = 0 8 x + 27 y - 14 = \pm \sqrt{169 y^{2} - 260 y + 292} (8 x + 27 y - 14)^{2} = {(y - \frac{10}{13})}^{2} + 192 (8 x + 27 y - 14)^{2} - {(y - \frac{10}{13})}^{2} = 192$

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