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

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

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

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

(h, k) = (- 1, 3), a = 3, b = 32

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 1, 3), a = 3, b = 32

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 1, 3), b = 32, a = 3

\frac{( x - 8 ) ^{2}}{16} + \frac{( y + 1 ) ^{2}}{81} = 1

36 x^{2} + 9 y^{2} + 48 x - 36 y - 72 = 0

(x - 5)^{2} + (y - 1)^{2} + (y - 1)^{2} = 14

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

\frac{( x - 3 ) ^{2}}{( 18 )} + \frac{( y + 1 ) ^{2}}{12} = 1

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