Question 1105803
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Apply completing the squares:


<pre>
   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


<U>Answer</U>.  A = 4,  B = 3,  C = 9,  D = 1, E = 0.
</pre>

Solved.


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On completing the square, see the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/Learning-by-examples-on-HOW-TO-complete-the-square.lesson>HOW TO complete the square - Learning by examples</A> 

in this site.