What is 9x^2+16y^2+72x+128y+256=0 ?

The solution to 9x^2+16y^2+72x+128y+256=0 is Ellipse with (h,k)=(-4,-4),a=4,b=3

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9x^2+16y^2+72x+128y+256=0

9 x^{2} + 16 y^{2} + 72 x + 128 y + 256 = 0

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

Solution steps

9 x^{2} + 16 y^{2} + 72 x + 128 y + 256 = 0

Rewrite

9 x^{2} + 16 y^{2} + 72 x + 128 y + 256 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

9 x^{2} + 4 y^{2} - 18 x - 16 y - 11 = 0

x^{2} + 4 y^{2} - 25 = 0

4 x^{2} + y^{2} + 2 y - 35 = 0

5 x^{2} + y^{2} - 20 x + 19 = 0

\frac{( x + 2 ) ^{2}}{16} + \frac{( y - 3 ) ^{2}}{4} = 1

What is 9x^2+16y^2+72x+128y+256=0 ?
The solution to 9x^2+16y^2+72x+128y+256=0 is Ellipse with (h,k)=(-4,-4),a=4,b=3