What is 9-x^2-9y^2>0 ?

The solution to 9-x^2-9y^2>0 is Ellipse with (h,k)=(0,0),a=3,b=1

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9-x^2-9y^2>0

9 - x^{2} - 9 y^{2} > 0

(h, k) = (0, 0), a = 3, b = 1

Solution steps

9 - x^{2} - 9 y^{2} > 0

Rewrite

9 - x^{2} - 9 y^{2} > 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 3, b = 1

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 3, b = 1

9 x^{2} + 16 y^{2} < 25

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

25 x^{2} + 9 y^{2} - 18 y - 216 = 0

\frac{x ^{2}}{63500} + \frac{y ^{2}}{50900} = 1

4 x^{2} + 9 y^{2} + 24 x - 36 y + 36 = 0

What is 9-x^2-9y^2>0 ?
The solution to 9-x^2-9y^2>0 is Ellipse with (h,k)=(0,0),a=3,b=1