What is 9x^2+11y^2=10 ?

The solution to 9x^2+11y^2=10 is Ellipse with (h,k)=(0,0),a=(sqrt(10))/3 ,b=sqrt(10/11)

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9x^2+11y^2=10

9 x^{2} + 11 y^{2} = 10

(h, k) = (0, 0), a = \frac{10}{3}, b = \frac{10}{11}

Solution steps

9 x^{2} + 11 y^{2} = 10

Rewrite

9 x^{2} + 11 y^{2} = 10

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{10}{3} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{10}{11} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{10}{3}, b = \frac{10}{11}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = \frac{10}{3}, b = \frac{10}{11}

16 x^{2} + 36 y^{2} + 32 x + 72 y - 524 = 0

\frac{1}{3} 3 x^{2} + 3 y^{2} - 8 x - 8 y \cdot 31 = 0

2 x^{2} + 3 y^{2} - 18 = 0

49 x^{2} + 16 y^{2} - 588 x + 128 y + 1236 = 0

18 x^{2} + 24 y + 12 y^{2} - 12 x = 1

What is 9x^2+11y^2=10 ?
The solution to 9x^2+11y^2=10 is Ellipse with (h,k)=(0,0),a=(sqrt(10))/3 ,b=sqrt(10/11)