What is 16x^2+25y^2-96x+50y-231=0 ?

The solution to 16x^2+25y^2-96x+50y-231=0 is Ellipse with (h,k)=(3,-1),a=5,b=4

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16x^2+25y^2-96x+50y-231=0

16 x^{2} + 25 y^{2} - 96 x + 50 y - 231 = 0

(h, k) = (3, - 1), a = 5, b = 4

Solution steps

16 x^{2} + 25 y^{2} - 96 x + 50 y - 231 = 0

Rewrite

16 x^{2} + 25 y^{2} - 96 x + 50 y - 231 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (3, - 1), a = 5, b = 4

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (3, - 1), a = 5, b = 4

(\frac{x ^{2}}{15}) + (\frac{y ^{2}}{16}) = 1

\frac{x ^{2}}{25} + \frac{z ^{2}}{64} = 1

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

\frac{x ^{2}}{64} + \frac{y ^{2}}{1} = 1

x^{2} + 4 y^{2} + 20 x - 40 y = - 100

What is 16x^2+25y^2-96x+50y-231=0 ?
The solution to 16x^2+25y^2-96x+50y-231=0 is Ellipse with (h,k)=(3,-1),a=5,b=4