What is 9x^2+y^2-81=0 ?

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

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9x^2+y^2-81=0

9 x^{2} + y^{2} - 81 = 0

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

Solution steps

9 x^{2} + y^{2} - 81 = 0

Rewrite

9 x^{2} + y^{2} - 81 = 0

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

16 x^{2} + 80 y^{2} = 1280

\frac{5 x ^{2} + y ^{2} - 15 x + 8 y - 11}{4} = 0

\frac{x ^{2} + y ^{2} + 4 x - 8 y - 6}{x ^{2} + y ^{2} + 6 x + 2 y + 9} = \frac{4}{5}

64 - 25 x^{2} - 4 y^{2} + 24 y \geq 0

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