What is 16x^2+36y^2-256x+576y+2752=0 ?

The solution to 16x^2+36y^2-256x+576y+2752=0 is Ellipse with (h,k)=(8,-8),a=6,b=4

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16x^2+36y^2-256x+576y+2752=0

16 x^{2} + 36 y^{2} - 256 x + 576 y + 2752 = 0

(h, k) = (8, - 8), a = 6, b = 4

Solution steps

16 x^{2} + 36 y^{2} - 256 x + 576 y + 2752 = 0

Rewrite

16 x^{2} + 36 y^{2} - 256 x + 576 y + 2752 = 0

in the form of the standard ellipse equation

\frac{( x - 8 ) ^{2}}{6 ^{2}} + \frac{( y - ( - 8 ) ) ^{2}}{4 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (8, - 8), a = 6, b = 4

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (8, - 8), a = 6, b = 4

16 x^{2} + 4 y^{2} + 32 x + 32 y + 16 = 0

x^{2} + 5 y^{2} = 150

36 x^{2} + 16 y^{2} = 49

81 X^{2} + 49 Y^{2} = 3969

9 x^{2} + 36 y^{2} - 64 x - 18 y - 71 = 36

What is 16x^2+36y^2-256x+576y+2752=0 ?
The solution to 16x^2+36y^2-256x+576y+2752=0 is Ellipse with (h,k)=(8,-8),a=6,b=4