SOLUTION: Find the Values of A,B,C,D and E so that each equation is an identity (Show your solution) 4x^2 - 9y^2

SOLUTION: 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

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(52797) (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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