What is 9x^2+16y^2+126x+96y+441=0 ?

The solution to 9x^2+16y^2+126x+96y+441=0 is Ellipse with (h,k)=(-7,-3),a=4,b=3

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9x^2+16y^2+126x+96y+441=0

9 x^{2} + 16 y^{2} + 126 x + 96 y + 441 = 0

(h, k) = (- 7, - 3), a = 4, b = 3

Solution steps

9 x^{2} + 16 y^{2} + 126 x + 96 y + 441 = 0

Rewrite

9 x^{2} + 16 y^{2} + 126 x + 96 y + 441 = 0

in the form of the standard ellipse equation

\frac{( x - ( - 7 ) ) ^{2}}{4 ^{2}} + \frac{( y - ( - 3 ) ) ^{2}}{3 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 7, - 3), a = 4, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 7, - 3), a = 4, b = 3

2 x^{2} + y^{2} - 10 = 0

3 x^{2} + 3 y^{2} + 12 y = 0

\frac{( x + 1 ) ^{2}}{22.33} + \frac{( y - 1 ) ^{2}}{16.75} = 1

\frac{x ^{2}}{25} + \frac{y ^{2}}{11} = 1

4 x^{2} + 2 y^{2} - 7 x + y - 5 = 0

What is 9x^2+16y^2+126x+96y+441=0 ?
The solution to 9x^2+16y^2+126x+96y+441=0 is Ellipse with (h,k)=(-7,-3),a=4,b=3