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Focii of Hyperbola

Trace the par...

Question

Trace the parabolas :
$16 x^{2} - 24 x y + 9 y^{2} + 32 x + 856 y - 39 = 0 .$

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Solution

Trace the equation
$16 x^{2} - 24 x y + 9 y^{2} + 32 x + 856 y - 39 = 0 4 x - 3 y + 4 = \pm \sqrt{55 - 880 y} (4 x - 3 y + 4)^{2} = 55 - 880 y = - 880 [y - \frac{1}{160}]$
Let
$4 x - 3 y + 4 = Y y - \frac{1}{160} = X$
$Y^{2} = - 880 X$

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