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

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

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9y^2=36-4x^2

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

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

Solution steps

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

Rewrite

9 y^{2} = 36 - 4 x^{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}}{98} + \frac{y ^{2}}{2} = 1

x^{2} + 4 y^{2} + 10 x - 8 y + 13 = 0

x^{2} + 4 y^{2} + 12 x = 0

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

\frac{( x - 3 ) ^{2}}{25} + \frac{( y + 2 ) ^{2}}{49} = 1

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