x^2-6x+16y^2+32y+9=0

Question

write this equation of ellipse in standard form

Answer 1

Hi Malak

 

The equation of an ellipse in standard form is 

 

[(x-h)²/a²] + [(y-k)²/b²] = 1

 

The equation given is

x²-6x+16y²+32y+9 = 0

 

x²-6x+9 = (x-3)²

so h = 3 

 

This leaves us with 16y²+32y

16(y²+2y)

To complete the square here, we need to add 1 (times 16) to both sides of the equation

16(y²+2y+1) = 16(y+1)²

where k = -1

 

Putting this together we have

 

(x-3)² + 16(y+1)² = 16

 

But for the standard for we need the right side of the equation to equal 1

So, divide by 16

 

(x-3)²/16 + (y+1)² = 1