What is 25y^2-x^2-150y-16x+109=0 ?

The solution to 25y^2-x^2-150y-16x+109=0 is Hyperbola with (h,k)=(-8,3),a=(2sqrt(13))/5 ,b=2sqrt(13)

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25y^2-x^2-150y-16x+109=0

25 y^{2} - x^{2} - 150 y - 16 x + 109 = 0

(h, k) = (- 8, 3), a = \frac{2 13}{5}, b = 213

Solution steps

25 y^{2} - x^{2} - 150 y - 16 x + 109 = 0

Rewrite

25 y^{2} - x^{2} - 150 y - 16 x + 109 = 0

in the form of a standard hyperbola equation

\frac{( y - 3 ) ^{2}}{( \frac{2 13}{5} ) ^{2}} - \frac{( x - ( - 8 ) ) ^{2}}{( 2 13 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- 8, 3), a = \frac{2 13}{5}, b = 213

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

- x^{2} + 36 y^{2} = 36

x^{2} - 4 y^{2} - 2 x - 16 y - 19 = 0

\frac{1}{x - y} + \frac{1}{x + y} = 5

\frac{( x - 8 ) ^{2}}{64} - \frac{( y - 9 ) ^{2}}{4} = 1

What is 25y^2-x^2-150y-16x+109=0 ?
The solution to 25y^2-x^2-150y-16x+109=0 is Hyperbola with (h,k)=(-8,3),a=(2sqrt(13))/5 ,b=2sqrt(13)