What is x^2+9y^2=18 ?

The solution to x^2+9y^2=18 is Ellipse with (h,k)=(0,0),a=3sqrt(2),b=sqrt(2)

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x^2+9y^2=18

x^{2} + 9 y^{2} = 18

(h, k) = (0, 0), a = 32, b = 2

Solution steps

x^{2} + 9 y^{2} = 18

Rewrite

x^{2} + 9 y^{2} = 18

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 32, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 32, b = 2

9 x^{2} + 4 y^{2} - 18 x + 8 y = 23

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

\frac{( x - 3 ) ^{2}}{64} + \frac{( y - 3 ) ^{2}}{16} = 1

4 x^{2} + y^{2} + 48 x + 128 = 0

\frac{( x - 2 ) ^{2}}{9} + \frac{( y + 4 ) ^{2}}{16} = 1

What is x^2+9y^2=18 ?
The solution to x^2+9y^2=18 is Ellipse with (h,k)=(0,0),a=3sqrt(2),b=sqrt(2)