What is 2x^2+8y^2=18 ?

The solution to 2x^2+8y^2=18 is Ellipse with (h,k)=(0,0),a=3,b= 3/2

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2x^2+8y^2=18

2 x^{2} + 8 y^{2} = 18

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

Solution steps

2 x^{2} + 8 y^{2} = 18

Rewrite

2 x^{2} + 8 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} + 8 y^{2} = 15

8 x^{2} + 4 y^{2} = 21

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

144 x^{2} + 169 y^{2} - 288 x + 676 y - 33516 = 0

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

What is 2x^2+8y^2=18 ?
The solution to 2x^2+8y^2=18 is Ellipse with (h,k)=(0,0),a=3,b= 3/2