What is 25y^2+250y-16x^2-32x+209=0 ?

The solution to 25y^2+250y-16x^2-32x+209=0 is Hyperbola with (h,k)=(-1,-5),a=4,b=5

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25y^2+250y-16x^2-32x+209=0

25 y^{2} + 250 y - 16 x^{2} - 32 x + 209 = 0

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

Solution steps

25 y^{2} + 250 y - 16 x^{2} - 32 x + 209 = 0

Rewrite

25 y^{2} + 250 y - 16 x^{2} - 32 x + 209 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

x^{2} - 2 y^{2} - 4 x - 4 y - 400 = 0

9 x^{2} - 16 y^{2} - 36 x - 32 y - 124 = 0

5 x^{2} - 4 y^{2} + 80 = 0

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

16 y^{2} - x^{2} + 2 x + 64 y - 1 = 0

What is 25y^2+250y-16x^2-32x+209=0 ?
The solution to 25y^2+250y-16x^2-32x+209=0 is Hyperbola with (h,k)=(-1,-5),a=4,b=5