What is 2x^2+y^2=72 ?

The solution to 2x^2+y^2=72 is Ellipse with (h,k)=(0,0),a=6,b=6sqrt(2)

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2x^2+y^2=72

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

(h, k) = (0, 0), a = 6, b = 62

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 6, b = 62

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 62, a = 6

81 x^{2} + 49 y^{2} + 1296 x + 196 y + 1411 = 0

\frac{y ^{2}}{4} + \frac{x ^{2}}{9} = 10

9 x^{2} + 16 y^{2} + 42 x - 24 y + 57 = 0

24 x^{2} + 9 y^{2} = 216

x^{2} + 4 y^{2} - 10 x + 16 y + 37 = 0

What is 2x^2+y^2=72 ?
The solution to 2x^2+y^2=72 is Ellipse with (h,k)=(0,0),a=6,b=6sqrt(2)