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

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

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9y^2+x^2=81

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

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

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

\frac{( x ^{2} )}{9} + \frac{( ( y - 1 ) ^{2} )}{25} = 1

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

x^{(2)} - 4 x + 3 y^{(2)} = - 2

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