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

The solution to y^2=36-4x^2 is Ellipse with (h,k)=(0,0),a=3,b=6

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y^2=36-4x^2

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

(h, k) = (0, 0), a = 3, b = 6

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 3, b = 6

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 6, a = 3

x^{2} + 3 y^{2} + 6 x + 6 = 0

(x^{2} + 8 (y + 5)^{2}) = 20

\frac{( x - 4 ) ^{2}}{25} + \frac{( y - 2 ) ^{2}}{16} = 1

9 x^{2} + 25 y^{2} - 36 x - 189 = 0

9 x^{2} + 25 y^{2} - 18 x - 150 y + 9 = 0

What is y^2=36-4x^2 ?
The solution to y^2=36-4x^2 is Ellipse with (h,k)=(0,0),a=3,b=6