What is 81x^2+9y^2=9 ?

The solution to 81x^2+9y^2=9 is Ellipse with (h,k)=(0,0),a= 1/3 ,b=1

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81x^2+9y^2=9

81 x^{2} + 9 y^{2} = 9

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

Solution steps

81 x^{2} + 9 y^{2} = 9

Rewrite

81 x^{2} + 9 y^{2} = 9

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

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

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

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

7 x^{2} + 25 y^{2} = 175

\frac{( x - 1 ) ^{2}}{16} + \frac{( y - 2 ) ^{2}}{9} = 1

What is 81x^2+9y^2=9 ?
The solution to 81x^2+9y^2=9 is Ellipse with (h,k)=(0,0),a= 1/3 ,b=1