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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

\frac{x ^{2}}{36} + \frac{y ^{2}}{81} = 1

4 x^{2} + 25 y^{2} - 40 x + 150 y + 225 = 0

36 x^{2} + y^{2} = 36

\frac{x ^{2}}{9} + \frac{y ^{2}}{1} = 1

h (x) = 6 x^{2} - 5 x + 7 h (x) (2 + h (x))

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