What is 25x^2+16y^2-50x+64y-311=0 ?

The solution to 25x^2+16y^2-50x+64y-311=0 is Ellipse with (h,k)=(1,-2),a=4,b=5

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25x^2+16y^2-50x+64y-311=0

25 x^{2} + 16 y^{2} - 50 x + 64 y - 311 = 0

(h, k) = (1, - 2), a = 4, b = 5

Solution steps

25 x^{2} + 16 y^{2} - 50 x + 64 y - 311 = 0

Rewrite

25 x^{2} + 16 y^{2} - 50 x + 64 y - 311 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (1, - 2), a = 4, b = 5

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (1, - 2), b = 5, a = 4

\frac{x ^{2}}{9} + \frac{y ^{2}}{8} = 1

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

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

\frac{x ^{2}}{5} + \frac{y ^{2}}{3} = 1

16 x^{2} + 25 y^{2} - 64 x + 150 y - 11 = 0

What is 25x^2+16y^2-50x+64y-311=0 ?
The solution to 25x^2+16y^2-50x+64y-311=0 is Ellipse with (h,k)=(1,-2),a=4,b=5