What is 16x^2+9y^2-32x+18y-119=0 ?

The solution to 16x^2+9y^2-32x+18y-119=0 is Ellipse with (h,k)=(1,-1),a=3,b=4

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16x^2+9y^2-32x+18y-119=0

16 x^{2} + 9 y^{2} - 32 x + 18 y - 119 = 0

(h, k) = (1, - 1), a = 3, b = 4

Solution steps

16 x^{2} + 9 y^{2} - 32 x + 18 y - 119 = 0

Rewrite

16 x^{2} + 9 y^{2} - 32 x + 18 y - 119 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (1, - 1), a = 3, b = 4

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (1, - 1), b = 4, a = 3

16 x^{2} + 36 y^{2} + 112 x - 108 y + 133 = 0

2 x^{2} + 11 y^{2} = 11

2 x^{2} + 3 y^{2} = 11

2 x^{2} + 3 y^{2} = 17

x^{2} + 4 y^{2} \leq 1

What is 16x^2+9y^2-32x+18y-119=0 ?
The solution to 16x^2+9y^2-32x+18y-119=0 is Ellipse with (h,k)=(1,-1),a=3,b=4