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

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

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36-9x^2-4y^2>= 0

36 - 9 x^{2} - 4 y^{2} \geq 0

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

Solution steps

36 - 9 x^{2} - 4 y^{2} \geq 0

Rewrite

36 - 9 x^{2} - 4 y^{2} \geq 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

(x 3)^{2} + (y + 2)^{2} = 25

(\frac{( y - 8 )}{40})^{2} + (\frac{( x + 10 )}{211})^{2} = 1

1 = (\frac{x}{84.5})^{2} + (\frac{y}{33.5})^{2}

2 x^{2} + 3 y^{2} = 6

4 x^{2} + 5 y^{2} + 16 x - 20 y + 16 = 0

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