What is (x+5)^2-(y-7)^2=1 ?

The solution to (x+5)^2-(y-7)^2=1 is Hyperbola with (h,k)=(-5,7),a=1,b=1

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(x+5)^2-(y-7)^2=1

(x + 5)^{2} - (y - 7)^{2} = 1

(h, k) = (- 5, 7), a = 1, b = 1

Solution steps

(x + 5)^{2} - (y - 7)^{2} = 1

Rewrite

(x + 5)^{2} - (y - 7)^{2} = 1

in the form of a standard hyperbola equation

\frac{( x - ( - 5 ) ) ^{2}}{1 ^{2}} - \frac{( y - 7 ) ^{2}}{1 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- 5, 7), a = 1, b = 1

\frac{1}{2} y^{2} - 2 y = \frac{3}{2} x^{2} - 5 x

\frac{x ^{2}}{49} - \frac{y ^{2}}{44} = 1

x^{2} - y^{2} = 640

- \frac{1}{2} (\frac{x ^{2}}{2} - 100 x) + C = - 3 y^{2} + 150 y + C

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

What is (x+5)^2-(y-7)^2=1 ?
The solution to (x+5)^2-(y-7)^2=1 is Hyperbola with (h,k)=(-5,7),a=1,b=1