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

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

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

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

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

Solution steps

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

Rewrite

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

(x - 2)^{2} + 4 y^{2} = 36

6 x^{2} + 2 y^{2} + 18 x - 10 y + 2 = 0

16 x^{2} + 9 y^{2} - 128 x - 18 y + 121 = 0

\frac{( x - 2 ) ^{2}}{9} + \frac{y ^{2}}{7} = 1

\frac{x ^{2}}{4} + \frac{y ^{2}}{36} = 1

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