Hi

 Standard Form of an Equation of an Ellipse is 

where Pt(h,k) is the center and a and b  are the respective vertices, distances from center.



Finding the center of the following ellipse:  

16x^2+4y^2+64x+24y+36=0

 16(x^2 + 4x) + 4(y^2+6y)+36 = 0   |completing the squares

 16[(x+2)^2 -4] + 4[(y+3)^2-9] + 36 = 0

 16(x+2)^2 - 64 + 4(y+3)^2 - 36 + 36 = 0

   16(x+2)^2 + 4(y+3)^2 = 64

   

center pt(-2,-3)





      

 

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