What is x^2+2y^2-6x+4y+7=0 ?

The solution to x^2+2y^2-6x+4y+7=0 is Ellipse with (h,k)=(3,-1),a=2,b=sqrt(2)

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x^2+2y^2-6x+4y+7=0

x^{2} + 2 y^{2} - 6 x + 4 y + 7 = 0

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

Solution steps

x^{2} + 2 y^{2} - 6 x + 4 y + 7 = 0

Rewrite

x^{2} + 2 y^{2} - 6 x + 4 y + 7 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

9 x^{2} + 16 y^{2} + 36 x - 160 y + 292 = 0

4 x^{2} + 9 y^{2} + 16 x - 54 y + 61 = 0

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

\frac{x ^{2}}{\frac{81}{4}} + \frac{y ^{2}}{\frac{25}{16}} = 1

9 x^{2} + 16 y^{2} + 72 x + 128 y + 256 = 0

What is x^2+2y^2-6x+4y+7=0 ?
The solution to x^2+2y^2-6x+4y+7=0 is Ellipse with (h,k)=(3,-1),a=2,b=sqrt(2)