What is 2x^2+3y^2+4x-6y-1=0 ?

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

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2x^2+3y^2+4x-6y-1=0

2 x^{2} + 3 y^{2} + 4 x - 6 y - 1 = 0

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

Solution steps

2 x^{2} + 3 y^{2} + 4 x - 6 y - 1 = 0

Rewrite

2 x^{2} + 3 y^{2} + 4 x - 6 y - 1 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

y^{2} = 100 - 25 x^{2}

36 - 4 x^{2} - 9 y^{2} < 0

4 (x + 1)^{2} + 3 (y - 1)^{2} = 48

2 x^{2} + y^{2} = 72

81 x^{2} + 49 y^{2} + 1296 x + 196 y + 1411 = 0

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