What is 4x^2-25y^2+8x-100y-196=0 ?

The solution to 4x^2-25y^2+8x-100y-196=0 is Hyperbola with (h,k)=(-1,-2),a=5,b=2

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4x^2-25y^2+8x-100y-196=0

4 x^{2} - 25 y^{2} + 8 x - 100 y - 196 = 0

(h, k) = (- 1, - 2), a = 5, b = 2

Solution steps

4 x^{2} - 25 y^{2} + 8 x - 100 y - 196 = 0

Rewrite

4 x^{2} - 25 y^{2} + 8 x - 100 y - 196 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (- 1, - 2), a = 5, b = 2

x, x \cdot (x + 1) = h (x)^{2}

- x^{2} + 2 y^{2} - 20 y - 6 = 0

\frac{( x - 1 ) ^{2}}{64} - \frac{( y - 2 ) ^{2}}{32} = 1

- x^{2} + 9 y^{2} - 36 y + 27 = 0

(\frac{y - 4}{16})^{2} - (\frac{x - 6}{4})^{2} = 1

What is 4x^2-25y^2+8x-100y-196=0 ?
The solution to 4x^2-25y^2+8x-100y-196=0 is Hyperbola with (h,k)=(-1,-2),a=5,b=2