What is 25y^2+9x^2-108x-200y+499=0 ?

The solution to 25y^2+9x^2-108x-200y+499=0 is Ellipse with (h,k)=(6,4),a=5,b=3

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

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

(h, k) = (6, 4), a = 5, b = 3

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - 6 ) ^{2}}{5 ^{2}} + \frac{( y - 4 ) ^{2}}{3 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (6, 4), a = 5, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (6, 4), a = 5, b = 3

50 = \frac{100}{1 + x ^{2} + y ^{2}}

9 x^{2} + 4 y^{2} - 36 x + 8 y + 31 = 0

\frac{x ^{2}}{1.586 9 ^{2}} + \frac{y ^{2}}{0.9989 8 ^{2}} = 1

9 x^{2} + 25 y^{2} + 90 x = 0

x^{2} + 2 y^{2} = 11

What is 25y^2+9x^2-108x-200y+499=0 ?
The solution to 25y^2+9x^2-108x-200y+499=0 is Ellipse with (h,k)=(6,4),a=5,b=3