What is (x-1)^2-(y-4)^2=16 ?

The solution to (x-1)^2-(y-4)^2=16 is Hyperbola with (h,k)=(1,4),a=4,b=4

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(x-1)^2-(y-4)^2=16

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

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

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

y^{2} = x^{2} + 289

- 3 y^{2} + 18 x^{2} = - y - 2

9 a^{2} - b^{2} + 81 = 13 a - 18 b - 81

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

x^{2} = 2 y^{2} + 6

What is (x-1)^2-(y-4)^2=16 ?
The solution to (x-1)^2-(y-4)^2=16 is Hyperbola with (h,k)=(1,4),a=4,b=4