What is 12x-3x^2+36y-6y^2>0 ?

The solution to 12x-3x^2+36y-6y^2>0 is Ellipse with (h,k)=(2,3),a=sqrt(22),b=sqrt(11)

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12x-3x^2+36y-6y^2>0

12 x - 3 x^{2} + 36 y - 6 y^{2} > 0

(h, k) = (2, 3), a = 22, b = 11

Solution steps

12 x - 3 x^{2} + 36 y - 6 y^{2} > 0

Rewrite

12 x - 3 x^{2} + 36 y - 6 y^{2} > 0

in the form of the standard ellipse equation

\frac{( x - 2 ) ^{2}}{( 22 ) ^{2}} + \frac{( y - 3 ) ^{2}}{( 11 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (2, 3), a = 22, b = 11

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (2, 3), a = 22, b = 11

16 x^{2} + 25 y^{2} + 64 x - 200 y + 64 = 0

5 x^{2} + 10 y^{2} + 125 x + 125 y + 44 = 0

\frac{( x - 1 ) ^{2}}{36} + \frac{( y - 3 ) ^{2}}{16} = 1

\frac{( x - 5 ) ^{2}}{25} + \frac{( y + 2 ) ^{2}}{9} = 1

\frac{( x - 7 ) ^{2}}{25} + \frac{( y + 9 ) ^{2}}{36} = 1

What is 12x-3x^2+36y-6y^2>0 ?
The solution to 12x-3x^2+36y-6y^2>0 is Ellipse with (h,k)=(2,3),a=sqrt(22),b=sqrt(11)