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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

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

\frac{2 x - x ^{2} - y ^{2}}{x ^{2} + y ^{2} - x} \leq 0

x^{2} + 2 - 6 x = - 5 z^{2} + 2

x^{2} + 2 y^{2} + 2 x - 2 y = 0

x, x^{2} + 5 Y (x)^{2} + 2 x - 30 Y + 36 = 0

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