What is 5x^2+2y^2+12y+8=0 ?

The solution to 5x^2+2y^2+12y+8=0 is Ellipse with (h,k)=(0,-3),a=sqrt(2),b=sqrt(5)

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5x^2+2y^2+12y+8=0

5 x^{2} + 2 y^{2} + 12 y + 8 = 0

(h, k) = (0, - 3), a = 2, b = 5

Solution steps

5 x^{2} + 2 y^{2} + 12 y + 8 = 0

Rewrite

5 x^{2} + 2 y^{2} + 12 y + 8 = 0

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( 2 ) ^{2}} + \frac{( y - ( - 3 ) ) ^{2}}{( 5 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, - 3), a = 2, b = 5

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, - 3), b = 5, a = 2

4 x^{2} + 5 y^{2} - 32 x + 30 y - 11 = 0

\frac{( x - 4 ) ^{2}}{100} + \frac{( y + 5 ) ^{2}}{49} = 1

5 y^{2} + z^{2} = 36

2 x^{(2)} + y^{(2)} = 1

16 - x^{2} - 9 y^{2} = - 1

What is 5x^2+2y^2+12y+8=0 ?
The solution to 5x^2+2y^2+12y+8=0 is Ellipse with (h,k)=(0,-3),a=sqrt(2),b=sqrt(5)