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

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

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

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

(h, k) = (4, 1), a = 5, b = 2

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

\frac{( x - 4 ) ^{2}}{5 ^{2}} - \frac{( y - 1 ) ^{2}}{2 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (4, 1), a = 5, b = 2

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

143 x^{2} - y^{2} + 152 x + 2 y + 164 = 0

15 x^{2} - 7 y^{2} + 3 x - 5 = 0

x^{2} - y^{2} + 1 > 0

4 x^{2} - y^{2} + 8 x + 6 y - 6 = 0

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