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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.

Sagot :

Panoyinidn
          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.
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