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

\frac{x ^{2}}{64} + \frac{y ^{2}}{49} = 1

\frac{x ^{2}}{36} + \frac{y ^{2}}{100} = 1

4 x^{2} + 16 y^{2} - 8 x - 96 y + 84 = 0

x^{2} + 4 y^{2} - 10 x - 40 y + 109 = 0

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