What is 16x^2+4y^2+32x+32y+16=0 ?

The solution to 16x^2+4y^2+32x+32y+16=0 is Ellipse with (h,k)=(-1,-4),a=2,b=4

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16x^2+4y^2+32x+32y+16=0

16 x^{2} + 4 y^{2} + 32 x + 32 y + 16 = 0

(h, k) = (- 1, - 4), a = 2, b = 4

Solution steps

16 x^{2} + 4 y^{2} + 32 x + 32 y + 16 = 0

Rewrite

16 x^{2} + 4 y^{2} + 32 x + 32 y + 16 = 0

in the form of the standard ellipse equation

\frac{( x - ( - 1 ) ) ^{2}}{2 ^{2}} + \frac{( y - ( - 4 ) ) ^{2}}{4 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 1, - 4), a = 2, b = 4

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 1, - 4), b = 4, a = 2

x^{2} + 5 y^{2} = 150

36 x^{2} + 16 y^{2} = 49

81 X^{2} + 49 Y^{2} = 3969

9 x^{2} + 36 y^{2} - 64 x - 18 y - 71 = 36

10 x^{2} + y + 2 x + y^{2} = 0

What is 16x^2+4y^2+32x+32y+16=0 ?
The solution to 16x^2+4y^2+32x+32y+16=0 is Ellipse with (h,k)=(-1,-4),a=2,b=4