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Find the centre, the foci, and the asymptotes of the hyperbola 4x2 - 9y2 -16x -...

Find the centre, the foci, and the asymptotes of the hyperbola 4x2 - 9y2 -16x - 54y = 101.

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Answer #1

4x2 - 9y2 -16x - 54y = 101

=> 4(x2 - 4x + 4) - 9(y2 + 6y + 9) + 65 = 101

=> 4(x - 2)2 - 9(y + 3)2 = 36

=> - = 1

=> - = 1

thus centre = (2, -3)

foci = (2+, -3) & (2-, -3) = (2+, -3) & (2-, -3) = (5.6055, -3) & (-1.6055, -3)

asymptotes : y = -3 + *(x-2) &  y = -3 - *(x-2)

thus asymptotes are y = - & y = - -

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