What is 2x^2+9y^2-18=0 ?

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

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2x^2+9y^2-18=0

2 x^{2} + 9 y^{2} - 18 = 0

(h, k) = (0, 0), a = 3, b = 2

Solution steps

2 x^{2} + 9 y^{2} - 18 = 0

Rewrite

2 x^{2} + 9 y^{2} - 18 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 3, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 3, b = 2

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

9 y^{2} + z^{2} = 16

\frac{x ^{2}}{2.8 9 ^{2}} + \frac{y ^{2}}{2.8 4 ^{2}} = 1

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

\frac{( x + 2 ) ^{2}}{16} + \frac{( y - 5 ) ^{2}}{4} = 1

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