What is 4x^{(2)}+9y^{(2)}=36 ?

The solution to 4x^{(2)}+9y^{(2)}=36 is Ellipse with (h,k)=(0,0),a=3,b=2

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

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

(h, k) = (0, 0), a = 3, b = 2

Solution steps

4 x^{2} + 9 y^{2} = 36

Rewrite

4 x^{2} + 9 y^{2} = 36

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 3, b = 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 = 2

\frac{( x - 2 ) ^{2}}{36} + \frac{( y - 6 ) ^{2}}{4} = 1

\frac{x ^{2}}{64} + \frac{y ^{2}}{81} = 1

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

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

9 y^{2} + 4 x^{2} = 36

What is 4x^{(2)}+9y^{(2)}=36 ?
The solution to 4x^{(2)}+9y^{(2)}=36 is Ellipse with (h,k)=(0,0),a=3,b=2