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astraxan [27]
3 years ago
15

What is the center of the equation X^2+y^2-4x-8y-16=0

Mathematics
1 answer:
Mice21 [21]3 years ago
6 0
                                            x² + y² - 4x - 8y - 16 = 0
                                                                      + 16 + 16
                                                   x² + y² - 4x - 8y = 16
                                                   x² - 4x + y² - 8y = 16
                                  (x² - 4x + 4) + (y² - 8y + 16) = 16 + 4 + 16
                   (x² - 2x - 2x + 4) + (y² - 4y - 4y + 16) = 20 + 16
[x(x) - x(2) - 2(x) - 2(-2)] + [y(y) - y(4) - 4(y) - 4(4)] = 36
                 [x(x - 2) - 2(x - 2)] + [y(y - 4) - 4(y - 4)] = 36
                                   (x - 2)(x - 2) + (y - 4)(y - 4) = 36
                                                  (x - 2)² + (y - 4)² = 36
                                                    36           36        36
                                          ¹/₃₆(x - 2)² + ¹/₃₆(y - 4)² = 1
Center: (2, 4)
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