What is x^2+2x+3y^2=6 ?

The solution to x^2+2x+3y^2=6 is Ellipse with (h,k)=(-1,0),a=sqrt(7),b=sqrt(7/3)

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x^2+2x+3y^2=6

x^{2} + 2 x + 3 y^{2} = 6

(h, k) = (- 1, 0), a = 7, b = \frac{7}{3}

Solution steps

x^{2} + 2 x + 3 y^{2} = 6

Rewrite

x^{2} + 2 x + 3 y^{2} = 6

in the form of the standard ellipse equation

\frac{( x - ( - 1 ) ) ^{2}}{( 7 ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{7}{3} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 1, 0), a = 7, b = \frac{7}{3}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 1, 0), a = 7, b = \frac{7}{3}

\frac{x ^{2}}{9} + \frac{y ^{2}}{81} = 1

- 4 x^{2} - y^{2} + 14 x - 5 y - 45 = 0

\frac{( x + 1 ) ^{2}}{20} + \frac{( y - 1 ) ^{2}}{36} = 1

\frac{( x - 2 ) ^{2}}{9} + \frac{( y + 5 ) ^{2}}{16} = 1

x^{2} + 8 y^{2} = 64

What is x^2+2x+3y^2=6 ?
The solution to x^2+2x+3y^2=6 is Ellipse with (h,k)=(-1,0),a=sqrt(7),b=sqrt(7/3)