What is 4x^2-25(y-1)^2=100 ?

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

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4x^2-25(y-1)^2=100

4 x^{2} - 25 (y - 1)^{2} = 100

(h, k) = (0, 1), a = 5, b = 2

Solution steps

4 x^{2} - 25 (y - 1)^{2} = 100

Rewrite

4 x^{2} - 25 (y - 1)^{2} = 100

in the form of a standard hyperbola equation

\frac{( x - 0 ) ^{2}}{5 ^{2}} - \frac{( y - 1 ) ^{2}}{2 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, 1), a = 5, b = 2

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

16 x^{2} - y^{2} - 32 x - 6 y - 57 = 0

\frac{y ^{2}}{25} - \frac{( x + 1 ) ^{2}}{16} = 1

6 x^{2} - 5 y^{2} + 36 x + 20 y - 16 = 0

5 x^{2} - 4 y^{2} = 2

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