Question 1105803: Find the Values of A,B,C,D and E so that each equation is an identity (Show your solution)
4x^2 - 9y^2 - 24x + 18y + 27 = A(x-B)^2 + C(y+D)^2 + E
Answer by ikleyn(52794)   (Show Source):
You can put this solution on YOUR website! .
Apply completing the squares:
4x^2 - 9y^2 - 24x + 18y + 27 =
= (4x^2 - 24x) - (9y^2 - 18y) + 27 =
= 4(x^2 - 6x) - 9*(y^2 - 2y) + 27 =
= 4*(x^2 - 6x + 9) - 9*(y^2 - 2y + 1) + 27 - 4*9 + 9*1 =
= 4*(x-3)^2 - 9*(y-1)^2 + 0.
Comparing it with the expression A(x-B)^2 + C(y+D)^2 + E, you can conclude that
Answer. A = 4, B = 3, C = 9, D = 1, E = 0.
Solved.
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On completing the square, see the lesson
- HOW TO complete the square - Learning by examples
in this site.
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