What is 4x^2+18y^2=72 ?

The solution to 4x^2+18y^2=72 is Ellipse with (h,k)=(0,0),a=3sqrt(2),b=2

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4x^2+18y^2=72

4 x^{2} + 18 y^{2} = 72

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

Solution steps

4 x^{2} + 18 y^{2} = 72

Rewrite

4 x^{2} + 18 y^{2} = 72

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

(y - 6)^{2} + 8 (x)^{2} = 64

\frac{( x + 1 ) ^{2}}{25} + \frac{( y + 2 ) ^{2}}{49} = 1

9 x^{2} + 4 y^{2} + 18 x - 8 y - 23 = 0

3 x^{2} + 4 y^{2} = 48

9 (x - 3)^{2} + 4 (y - 4)^{2} = 36

What is 4x^2+18y^2=72 ?
The solution to 4x^2+18y^2=72 is Ellipse with (h,k)=(0,0),a=3sqrt(2),b=2