What is 25x^2-16y^2+250x+32y+109=0 ?

The solution to 25x^2-16y^2+250x+32y+109=0 is Hyperbola with (h,k)=(-5,1),a=2sqrt(5),b=(5sqrt(5))/2

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25x^2-16y^2+250x+32y+109=0

25 x^{2} - 16 y^{2} + 250 x + 32 y + 109 = 0

(h, k) = (- 5, 1), a = 25, b = \frac{5 5}{2}

Solution steps

25 x^{2} - 16 y^{2} + 250 x + 32 y + 109 = 0

Rewrite

25 x^{2} - 16 y^{2} + 250 x + 32 y + 109 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (- 5, 1), a = 25, b = \frac{5 5}{2}

16 y^{2} - x^{2} + 2 x + 64 y + 47 = 0

x^{2} + 2 x - y^{2} + 6 y = 15

5 x^{2} - 4 y^{2} - 20 x + 24 y - 36 = 0

x^{2} - 2 x + 1 = 2 k (x) (k (x) - 2)

16 x^{2} - 25 y^{2} = 100

What is 25x^2-16y^2+250x+32y+109=0 ?
The solution to 25x^2-16y^2+250x+32y+109=0 is Hyperbola with (h,k)=(-5,1),a=2sqrt(5),b=(5sqrt(5))/2