What is x^2+2y^2+4x-8y-6=0 ?

The solution to x^2+2y^2+4x-8y-6=0 is Ellipse with (h,k)=(-2,2),a=3sqrt(2),b=3

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x^2+2y^2+4x-8y-6=0

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

(h, k) = (- 2, 2), a = 32, b = 3

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 2, 2), a = 32, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 2, 2), a = 32, b = 3

8 x^{2} + 2 y^{2} - 32 = 0

\frac{( x - 3 ) ^{2}}{5} + \frac{( y + 1 ) ^{2}}{9} = 1

16 x^{2} + 25 y^{2} - 96 x - 250 y + 369 = 0

9 (x + 4)^{2} + 13 (y - 1)^{2} = 117

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

What is x^2+2y^2+4x-8y-6=0 ?
The solution to x^2+2y^2+4x-8y-6=0 is Ellipse with (h,k)=(-2,2),a=3sqrt(2),b=3