The standard form of the given equation was reduced, representing an ellipse.
The given equation is:
[tex]4x^{2} +9y^{2} +24x-36y+36=0[/tex]
What is an equation?
An equation is a statement that equates to two expressions.
We know the above equation represents an ellipse.
Rearranging the given equation
[tex]4x^{2} +24x+9y^{2} -36y+36=0[/tex]
[tex]4(x^2+6x)+9(y^{2} -4y)+36=0[/tex]
[tex]4(x^2+6x+9)+9(y^{2} -4y+4)=36[/tex]
[tex]4(x+3)^2+9(y-2)^2=36[/tex]
[tex]\frac{4(x+3)^2}{36}+\frac{9(y-2)^2}{36} =1[/tex]
[tex]\frac{(x+3)^2}{9}+\frac{(y-2)^2}{4} =1[/tex], which is the standard form of the given equation.
Hence, the standard form of the given equation was reduced.
To get more about an ellipse visit:
https://brainly.com/question/450229
