What is 2x^2+4y^2=18 ?

The solution to 2x^2+4y^2=18 is Ellipse with (h,k)=(0,0),a=3,b= 3/(sqrt(2))

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2x^2+4y^2=18

2 x^{2} + 4 y^{2} = 18

(h, k) = (0, 0), a = 3, b = \frac{3}{2}

Solution steps

2 x^{2} + 4 y^{2} = 18

Rewrite

2 x^{2} + 4 y^{2} = 18

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 3, b = \frac{3}{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 = \frac{3}{2}

2 x^{2} + 4 y^{2} = 16

4 x^{2} + 9 y^{2} = 72

4 x^{2} + y^{2} - 8 x + 6 y + 1 = 0

9 (x + 2)^{2} + 4 (y - 1)^{2} - 36 = 0

9 x^{2} + y^{2} - 54 x - 8 y + 88 = 0

What is 2x^2+4y^2=18 ?
The solution to 2x^2+4y^2=18 is Ellipse with (h,k)=(0,0),a=3,b= 3/(sqrt(2))