What is 16x^2+81y^2=81 ?

The solution to 16x^2+81y^2=81 is Ellipse with (h,k)=(0,0),a= 9/4 ,b=1

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16x^2+81y^2=81

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

(h, k) = (0, 0), a = \frac{9}{4}, b = 1

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{9}{4} ) ^{2}} + \frac{( y - 0 ) ^{2}}{1 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{9}{4}, b = 1

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = \frac{9}{4}, b = 1

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

\frac{( x + 1 ) ^{2}}{5} + \frac{( y - 3 ) ^{2}}{9} = 1

16 - 2 x^{2} - y^{2} > 0

x^{2} + 2 y^{2} + 4 x - 8 y - 6 = 0

8 x^{2} + 2 y^{2} - 32 = 0

What is 16x^2+81y^2=81 ?
The solution to 16x^2+81y^2=81 is Ellipse with (h,k)=(0,0),a= 9/4 ,b=1