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

The solution to x^2+2y^2+8x-4y-6=0 is Ellipse with (h,k)=(-4,1),a=2sqrt(6),b=2sqrt(3)

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

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

(h, k) = (- 4, 1), a = 26, b = 23

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - ( - 4 ) ) ^{2}}{( 2 6 ) ^{2}} + \frac{( y - 1 ) ^{2}}{( 2 3 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 4, 1), a = 26, b = 23

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 4, 1), a = 26, b = 23

(\frac{y - 4}{16})^{2} + (\frac{x - 6}{4})^{2} = 1

8 x^{2} + y^{2} - 32 x - 16 y = - 16

6 x^{2} + 3 y^{2} + 3 y + 6 x = 15

\frac{x ^{2}}{16} + \frac{y ^{2}}{48} = 1

9^{2} x^{2} + 7^{2} y^{2} = 1

What is x^2+2y^2+8x-4y-6=0 ?
The solution to x^2+2y^2+8x-4y-6=0 is Ellipse with (h,k)=(-4,1),a=2sqrt(6),b=2sqrt(3)