What is 3x^2+6y^2=18 ?

The solution to 3x^2+6y^2=18 is Ellipse with (h,k)=(0,0),a=sqrt(6),b=sqrt(3)

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3x^2+6y^2=18

3 x^{2} + 6 y^{2} = 18

(h, k) = (0, 0), a = 6, b = 3

Solution steps

3 x^{2} + 6 y^{2} = 18

Rewrite

3 x^{2} + 6 y^{2} = 18

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( 6 ) ^{2}} + \frac{( y - 0 ) ^{2}}{( 3 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 6, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 6, b = 3

x^{2} = - 12 y

y^{2} = 4 x

x^{2} = - 8 y

y^{2} = - 25 x

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

What is 3x^2+6y^2=18 ?
The solution to 3x^2+6y^2=18 is Ellipse with (h,k)=(0,0),a=sqrt(6),b=sqrt(3)