What is 16x^2+9y^2-36y=108 ?

The solution to 16x^2+9y^2-36y=108 is Ellipse with (h,k)=(0,2),a=3,b=4

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16x^2+9y^2-36y=108

16 x^{2} + 9 y^{2} - 36 y = 108

(h, k) = (0, 2), a = 3, b = 4

Solution steps

16 x^{2} + 9 y^{2} - 36 y = 108

Rewrite

16 x^{2} + 9 y^{2} - 36 y = 108

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{3 ^{2}} + \frac{( y - 2 ) ^{2}}{4 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 2), a = 3, b = 4

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 2), b = 4, a = 3

3 x^{2} + 12 y^{2} - 6 x - 48 y + 33 = 0

x^{(2)} + 4 y^{(2)} + 2 x - 12 y + 6 = 0

2 x - x^{2} - 4 y^{2} - 16 y - 1 > 0

\frac{x ^{2}}{36} + \frac{y ^{2}}{64} = 1

25 x^{2} + 16 y^{2} - 50 x + 64 y - 311 = 0

What is 16x^2+9y^2-36y=108 ?
The solution to 16x^2+9y^2-36y=108 is Ellipse with (h,k)=(0,2),a=3,b=4