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

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

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

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

(h, k) = (0, 0), a = \frac{4 2}{3}, b = 22

Solution steps

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

Rewrite

4 - 36 + 9 x^{2} + 4 y^{2} = 0

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{4 2}{3} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( 2 2 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{4 2}{3}, b = 22

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 22, a = \frac{4 2}{3}

9 x^{2} + 25 y^{2} - 18 x - 100 y - 116 = 0

\frac{x ^{2}}{8} + \frac{y ^{2}}{5} = 1

x^{2} + 20 y^{2} - 2 x - 5 y = 0

9 x^{2} + 4 y^{2} - 36 x + 40 y + 100 = 0

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

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