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

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

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

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

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

Solution steps

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

Rewrite

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

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

\frac{( x + 7 ) ^{2}}{16} + \frac{( y + 5 ) ^{2}}{4} = 1

x^{2} + 3 \cdot y^{2} = 84

y^{2} = 9 - 4 x^{2}

25 x^{2} + 16 y^{2} - 150 x + 64 y = 111

\frac{x ^{2}}{25} + \frac{y ^{2}}{1} = 1

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