What is 8x^2+y^2+4y=0 ?

The solution to 8x^2+y^2+4y=0 is Ellipse with (h,k)=(0,-2),a=sqrt(1/2),b=2

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8x^2+y^2+4y=0

8 x^{2} + y^{2} + 4 y = 0

(h, k) = (0, - 2), a = \frac{1}{2}, b = 2

Solution steps

8 x^{2} + y^{2} + 4 y = 0

Rewrite

8 x^{2} + y^{2} + 4 y = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, - 2), a = \frac{1}{2}, b = 2

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, - 2), b = 2, a = \frac{1}{2}

4 x^{2} + 6 y^{2} - 8 x + 4 y - 6 \geq 0

25 x^{2} + 4 y^{2} + 200 x - 8 y + 304 = 0

(x - 3)^{2} + 16 (y - 2)^{2} = 16

\frac{( 2 x + 1 ) ^{2}}{4} + \frac{( 3 y - 2 ) ^{2}}{16} = 1

\frac{( x + 1 ) ^{2}}{100} + \frac{( y + 2 ) ^{2}}{121} = 1

What is 8x^2+y^2+4y=0 ?
The solution to 8x^2+y^2+4y=0 is Ellipse with (h,k)=(0,-2),a=sqrt(1/2),b=2