What is 9x^2+4y^2-18x+16y-119=0 ?

The solution to 9x^2+4y^2-18x+16y-119=0 is Ellipse with (h,k)=(1,-2),a=4,b=6

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9x^2+4y^2-18x+16y-119=0

9 x^{2} + 4 y^{2} - 18 x + 16 y - 119 = 0

(h, k) = (1, - 2), a = 4, b = 6

Solution steps

9 x^{2} + 4 y^{2} - 18 x + 16 y - 119 = 0

Rewrite

9 x^{2} + 4 y^{2} - 18 x + 16 y - 119 = 0

in the form of the standard ellipse equation

\frac{( x - 1 ) ^{2}}{4 ^{2}} + \frac{( y - ( - 2 ) ) ^{2}}{6 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (1, - 2), a = 4, b = 6

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (1, - 2), b = 6, a = 4

25 x^{2} + 9 y^{2} - 100 x + 18 x - 116 = 0

\frac{( x - 4 ) ^{2}}{25} + \frac{( y + 6 ) ^{2}}{4} = 1

4 x^{2} + 9 y^{2} - 16 x - 18 y = 11

\frac{x ^{2}}{9} + \frac{z ^{2}}{49} = 1

x^{2} + 2 x + 4 y^{2} - 16 y + 1 = 0

What is 9x^2+4y^2-18x+16y-119=0 ?
The solution to 9x^2+4y^2-18x+16y-119=0 is Ellipse with (h,k)=(1,-2),a=4,b=6