What is 16x^2+25y^2-96x+100y-156=0 ?

The solution to 16x^2+25y^2-96x+100y-156=0 is Ellipse with (h,k)=(3,-2),a=5,b=4

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16x^2+25y^2-96x+100y-156=0

16 x^{2} + 25 y^{2} - 96 x + 100 y - 156 = 0

(h, k) = (3, - 2), a = 5, b = 4

Solution steps

16 x^{2} + 25 y^{2} - 96 x + 100 y - 156 = 0

Rewrite

16 x^{2} + 25 y^{2} - 96 x + 100 y - 156 = 0

in the form of the standard ellipse equation

\frac{( x - 3 ) ^{2}}{5 ^{2}} + \frac{( y - ( - 2 ) ) ^{2}}{4 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (3, - 2), a = 5, b = 4

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (3, - 2), a = 5, b = 4

10 x^{2} + 4 y^{2} - 8 x - 10 y - 12 = 0

x^{2} + 4 y^{2} - 6 x + 8 y - 3 = 0

9 x^{2} + 25 y^{2} + 108 x - 200 y + 499 = 0

25 x^{2} + 36 y^{2} + 100 x + 72 y - 764 = 0

\frac{2 x ^{2}}{25} + \frac{( y - 3 ) ^{2}}{49} = 1

What is 16x^2+25y^2-96x+100y-156=0 ?
The solution to 16x^2+25y^2-96x+100y-156=0 is Ellipse with (h,k)=(3,-2),a=5,b=4