What is 4x^2+2y^2-8x+12y+6=0 ?

The solution to 4x^2+2y^2-8x+12y+6=0 is Ellipse with (h,k)=(1,-3),a=2,b=2sqrt(2)

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4x^2+2y^2-8x+12y+6=0

4 x^{2} + 2 y^{2} - 8 x + 12 y + 6 = 0

(h, k) = (1, - 3), a = 2, b = 22

Solution steps

4 x^{2} + 2 y^{2} - 8 x + 12 y + 6 = 0

Rewrite

4 x^{2} + 2 y^{2} - 8 x + 12 y + 6 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (1, - 3), a = 2, b = 22

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (1, - 3), b = 22, a = 2

\frac{( x + 3 ) ^{2}}{25} + \frac{( y - 8 ) ^{2}}{16} = 1

16 x^{2} + 9 y^{2} - 36 y = 108

3 x^{2} + 12 y^{2} - 6 x - 48 y + 33 = 0

x^{(2)} + 4 y^{(2)} + 2 x - 12 y + 6 = 0

2 x - x^{2} - 4 y^{2} - 16 y - 1 > 0

What is 4x^2+2y^2-8x+12y+6=0 ?
The solution to 4x^2+2y^2-8x+12y+6=0 is Ellipse with (h,k)=(1,-3),a=2,b=2sqrt(2)