What is 2x^2+y^2-4x+6y+3=0 ?

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

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2x^2+y^2-4x+6y+3=0

2 x^{2} + y^{2} - 4 x + 6 y + 3 = 0

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

Solution steps

2 x^{2} + y^{2} - 4 x + 6 y + 3 = 0

Rewrite

2 x^{2} + y^{2} - 4 x + 6 y + 3 = 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

25 x^{2} + 4 y^{2} - 250 x - 16 y + 541 = 0

x^{2} + 4 y^{2} - 6 x + 8 y + 9 = 0

16 x^{2} + 25 y^{2} - 96 x + 100 y - 156 = 0

10 x^{2} + 4 y^{2} - 8 x - 10 y - 12 = 0

x^{2} + 4 y^{2} - 6 x + 8 y - 3 = 0

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