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 ^{2} - 2 x + 1 )}{34} + \frac{( y ^{2} - 8 y + 16 )}{25} = 1

y^{2} \leq - 4 x^{2} + 4

\frac{( x - 4 ) ^{2}}{35} + \frac{( y - 2 ) ^{2}}{39} = 1

16 - 4 x^{2} - y^{2} > 0

\frac{( X - 7 ) ^{2}}{25} + \frac{( Y - 3 ) ^{2}}{16} = 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