What is 3x^2+y^2+2y-8=0 ?

The solution to 3x^2+y^2+2y-8=0 is Ellipse with (h,k)=(0,-1),a=sqrt(3),b=3

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3x^2+y^2+2y-8=0

3 x^{2} + y^{2} + 2 y - 8 = 0

(h, k) = (0, - 1), a = 3, b = 3

Solution steps

3 x^{2} + y^{2} + 2 y - 8 = 0

Rewrite

3 x^{2} + y^{2} + 2 y - 8 = 0

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( 3 ) ^{2}} + \frac{( y - ( - 1 ) ) ^{2}}{3 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, - 1), a = 3, b = 3

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, - 1), b = 3, a = 3

\frac{( x - 1 ) ^{2}}{25} + \frac{( y + 2 ) ^{2}}{16} = 1

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

12 x^{2} + 96 x + 5 y^{2} + 50 y + 257 = 0

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

\frac{( x - 2 ) ^{2}}{81} + \frac{( y + 5 ) ^{2}}{64} = 1

What is 3x^2+y^2+2y-8=0 ?
The solution to 3x^2+y^2+2y-8=0 is Ellipse with (h,k)=(0,-1),a=sqrt(3),b=3