What is 25x^2-9y^2-200x+36y+139=0 ?

The solution to 25x^2-9y^2-200x+36y+139=0 is Hyperbola with (h,k)=(4,2),a=3,b=5

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25x^2-9y^2-200x+36y+139=0

25 x^{2} - 9 y^{2} - 200 x + 36 y + 139 = 0

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

Solution steps

25 x^{2} - 9 y^{2} - 200 x + 36 y + 139 = 0

Rewrite

25 x^{2} - 9 y^{2} - 200 x + 36 y + 139 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

- 8 x^{2} + 4 y^{2} + 10 x - 6 y - 8 = 0

\frac{( x + 2 ) ^{2}}{9} - \frac{( y - 1 ) ^{2}}{16} = 1

16 x^{2} - 9 y^{2} - 64 x - 18 y + 199 = 0

4 x^{2} - 8 y^{2} = 3

y^{2} = x^{2} + 9

What is 25x^2-9y^2-200x+36y+139=0 ?
The solution to 25x^2-9y^2-200x+36y+139=0 is Hyperbola with (h,k)=(4,2),a=3,b=5