What is 50y^2-25x^2+100x-100y-75=0 ?

The solution to 50y^2-25x^2+100x-100y-75=0 is Hyperbola with (h,k)=(2,1),a=sqrt(1/2),b=1

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50y^2-25x^2+100x-100y-75=0

50 y^{2} - 25 x^{2} + 100 x - 100 y - 75 = 0

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

Solution steps

50 y^{2} - 25 x^{2} + 100 x - 100 y - 75 = 0

Rewrite

50 y^{2} - 25 x^{2} + 100 x - 100 y - 75 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

144 y^{(2)} - 25 x^{(2)} = 3600

16 y^{2} - 25 x^{2} = 1600

x, m (x)^{2} + 8 m (x) + 16 = 1 + x^{2}

(x - 5) (x - 1) = yy

\frac{( y + 3 ) ^{2}}{16} - \frac{( x + 4 ) ^{2}}{9} = 1

What is 50y^2-25x^2+100x-100y-75=0 ?
The solution to 50y^2-25x^2+100x-100y-75=0 is Hyperbola with (h,k)=(2,1),a=sqrt(1/2),b=1