What is 36-4x^2-9y^2<0 ?

The solution to 36-4x^2-9y^2<0 is Ellipse with (h,k)=(0,0),a=3,b=2

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36-4x^2-9y^2<0

36 - 4 x^{2} - 9 y^{2} < 0

(h, k) = (0, 0), a = 3, b = 2

Solution steps

36 - 4 x^{2} - 9 y^{2} < 0

Rewrite

36 - 4 x^{2} - 9 y^{2} < 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 3, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 3, b = 2

4 (x + 1)^{2} + 3 (y - 1)^{2} = 48

2 x^{2} + y^{2} = 72

81 x^{2} + 49 y^{2} + 1296 x + 196 y + 1411 = 0

\frac{y ^{2}}{4} + \frac{x ^{2}}{9} = 10

9 x^{2} + 16 y^{2} + 42 x - 24 y + 57 = 0

What is 36-4x^2-9y^2<0 ?
The solution to 36-4x^2-9y^2<0 is Ellipse with (h,k)=(0,0),a=3,b=2