What is (6(x)^2-12x)+((y)^2+4y)=-4 ?

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

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

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

(h, k) = (1, - 2), a = 1, b = 6

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - 1 ) ^{2}}{1 ^{2}} + \frac{( y - ( - 2 ) ) ^{2}}{( 6 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (1, - 2), a = 1, b = 6

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (1, - 2), b = 6, a = 1

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

x^{2} + 3 y^{2} - 4 x - 23 = 0

25 x^{2} + 9 y^{2} - 200 x + 90 y + 400 = 0

x^{2} + 4 y^{2} = 2

x^{2} + 2 y^{2} - 3 x + 4 y + 0.25 = 0

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