What is 3(x+1)^2+(y-1)^2=6 ?

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

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3(x+1)^2+(y-1)^2=6

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

\frac{x ^{2} + y ^{2} - x}{2 x - x ^{2} - y ^{2}} = 0

7 x^{2} + 16 y^{2} - 14 x - 64 y - 41 = 0

0 = \frac{1}{2} x^{2} - 1 + \frac{1}{4} y^{2}

4 x^{(2)} + 9 y^{(2)} = 36

\frac{( x - 2 ) ^{2}}{36} + \frac{( y - 6 ) ^{2}}{4} = 1

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