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

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

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9x^2+y^2=81

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

(h, k) = (0, 0), a = 3, b = 9

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{3 ^{2}} + \frac{( y - 0 ) ^{2}}{9 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 3, b = 9

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 9, a = 3

\frac{( x + 1 ) ^{2}}{9} + \frac{( y - 2 ) ^{2}}{4} = 1

\frac{( x - 3 ) ^{2}}{16} + \frac{( y + 4 ) ^{2}}{9} = 1

9 x^{2} + 4 y^{2} + 18 x - 16 y - 11 = 0

3 x^{2} + 2 y^{2} - 12 x + 8 y + 19 = 0

\frac{( x + 1 ) ^{2}}{4} + \frac{( y - 5 ) ^{2}}{9} = 1

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