You can put this solution on YOUR website! Classify this conic section and write it in standard form.
-2y^2-24y+72x-432=0
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Divide thru by -2:
y^2 + 12y -36x + 216 = 0
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y^2 + 12y + 36 + 180 = 36x
(y+6)^2 + 180 = 36x
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x = (1/36)(y+6)^2 + 5
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Parabola opening to the right.
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Cheers,
Stan H.