What is 4x^2=36-9y^2 ?

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

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4x^2=36-9y^2

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

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

Solution steps

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

Rewrite

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

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

25 x^{2} + 16 y^{2} + 100 x - 96 y - 154 = 0

\frac{( x + 1 ) ^{2}}{25} + \frac{( y + 5 ) ^{2}}{16} = 1

49 x^{2} + 25 y^{2} - 1225 = 0

15 x^{2} + 12 y^{2} + 30 x - 24 y = 150

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