What is 3x^2-6x+y^2+4y-11=0 ?

The solution to 3x^2-6x+y^2+4y-11=0 is Ellipse with (h,k)=(1,-2),a=sqrt(6),b=3sqrt(2)

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3x^2-6x+y^2+4y-11=0

3 x^{2} - 6 x + y^{2} + 4 y - 11 = 0

(h, k) = (1, - 2), a = 6, b = 32

Solution steps

3 x^{2} - 6 x + y^{2} + 4 y - 11 = 0

Rewrite

3 x^{2} - 6 x + y^{2} + 4 y - 11 = 0

in the form of the standard ellipse equation

\frac{( x - 1 ) ^{2}}{( 6 ) ^{2}} + \frac{( y - ( - 2 ) ) ^{2}}{( 3 2 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (1, - 2), a = 6, b = 32

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (1, - 2), b = 32, a = 6

7 x^{2} + 16 y^{2} + 28 x - 128 y + 172 = 0

\frac{( x + 2 ) ^{2}}{16} + \frac{y ^{2}}{49} = 1

9 x^{2} + 36 x + y^{2} + 2 y + 36 = 0

4 y^{2} + x^{2} = 8

\frac{x ^{2}}{3} + \frac{y ^{2}}{5} = 1

What is 3x^2-6x+y^2+4y-11=0 ?
The solution to 3x^2-6x+y^2+4y-11=0 is Ellipse with (h,k)=(1,-2),a=sqrt(6),b=3sqrt(2)