What is 11x^2+9y^2=1 ?

The solution to 11x^2+9y^2=1 is Ellipse with (h,k)=(0,0),a=sqrt(1/11),b= 1/3

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11x^2+9y^2=1

11 x^{2} + 9 y^{2} = 1

(h, k) = (0, 0), a = \frac{1}{11}, b = \frac{1}{3}

Solution steps

11 x^{2} + 9 y^{2} = 1

Rewrite

11 x^{2} + 9 y^{2} = 1

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{1}{11} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{1}{3} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{1}{11}, b = \frac{1}{3}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = \frac{1}{3}, a = \frac{1}{11}

x^{2} + y^{2} + 36 y = 0

x^{2} + 9 y^{2} - 2 x + 72 y + 136 = 0

36 x^{2} + 25 y^{2} - 50 y - 875 = 0

\frac{( x - 7 ) ^{2}}{64} + \frac{( y - 6 ) ^{2}}{36} = 1

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

What is 11x^2+9y^2=1 ?
The solution to 11x^2+9y^2=1 is Ellipse with (h,k)=(0,0),a=sqrt(1/11),b= 1/3