What is 8x^2+8y^2+16y=0 ?

The solution to 8x^2+8y^2+16y=0 is Ellipse with (h,k)=(0,-1),a=1,b=1

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8x^2+8y^2+16y=0

8 x^{2} + 8 y^{2} + 16 y = 0

(h, k) = (0, - 1), a = 1, b = 1

Solution steps

8 x^{2} + 8 y^{2} + 16 y = 0

Rewrite

8 x^{2} + 8 y^{2} + 16 y = 0

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{1 ^{2}} + \frac{( y - ( - 1 ) ) ^{2}}{1 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, - 1), a = 1, b = 1

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, - 1), b = 1, a = 1

\frac{x ^{2} + 12 x + 36}{100} + \frac{y ^{2}}{64} = 1

\frac{( x + 3 ) ^{2}}{4} + \frac{( y + 1 ) ^{2}}{9} = 1

1 = 4 x^{2} + 2 y^{2}

x^{2} + 2 y^{2} - 6 y = 18

\frac{( x - 4 ) ^{2}}{32} + \frac{( y - 3 ) ^{2}}{36} = 1

What is 8x^2+8y^2+16y=0 ?
The solution to 8x^2+8y^2+16y=0 is Ellipse with (h,k)=(0,-1),a=1,b=1