25x^2+9y^2+72y-81=0. Find the standard form of the equation by completing the square. Then identify and graph each conic.

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10-05-2015
Mathematics

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25x^2+9y^2+72y-81=0. Find the standard form of the equation by completing the square. Then identify and graph each conic.

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Panoyin Panoyin · Answer 1 · 2015-05-12T03:58:50+02:00

        25x² + 9y² + 72y - 81 = 0
   25x² + 9y² + 72y - 81 + 81 = 0 + 81
           25x² + 9y² + 72y = 81
           25x² + 9(y² + 8y + 16) = 81 + 9(16)
       25x² + 9(y² + 4y + 4y + 16) = 81 + 144
   25x² + 9(y(y) + 4(y) + 4(y) + 4(4)) = 225
      25x² + 9(y(y + 4) + 4(y + 4)) = 225
      25x² + 9(y + 4)(y + 4) = 225
           25x² + 9(y + 4)² = 225
   225    225    225
      x² + 9(y + 4)² = 1
   25 25

The conic section is an ellipse.