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

The solution to 4x^2+y^2=72 is Ellipse with (h,k)=(0,0),a=3sqrt(2),b=6sqrt(2)

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4x^2+y^2=72

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

(h, k) = (0, 0), a = 32, b = 62

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( 3 2 ) ^{2}} + \frac{( y - 0 ) ^{2}}{( 6 2 ) ^{2}} = 1

Therefore ellipse properties are:

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

64 x^{2} + 25 y^{2} - 16 x - 16 y - 648 = 0

\frac{( x - 3 ) ^{2}}{25} + \frac{( y + 1 ) ^{2}}{16} = 1

3 x^{2} + 4 y^{2} = 12

25 x^{2} + 16 y^{2} - 150 x + 128 y + 81 = 0

25 x^{2} + y^{2} - 100 x + 8 y + 91 = 0

What is 4x^2+y^2=72 ?
The solution to 4x^2+y^2=72 is Ellipse with (h,k)=(0,0),a=3sqrt(2),b=6sqrt(2)