What is (x-9)^2-9(y+7)^2=1 ?

The solution to (x-9)^2-9(y+7)^2=1 is Hyperbola with (h,k)=(9,-7),a=1,b= 1/3

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(x-9)^2-9(y+7)^2=1

(x - 9)^{2} - 9 (y + 7)^{2} = 1

(h, k) = (9, - 7), a = 1, b = \frac{1}{3}

Solution steps

(x - 9)^{2} - 9 (y + 7)^{2} = 1

Rewrite

(x - 9)^{2} - 9 (y + 7)^{2} = 1

in the form of a standard hyperbola equation

\frac{( x - 9 ) ^{2}}{1 ^{2}} - \frac{( y - ( - 7 ) ) ^{2}}{( \frac{1}{3} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (9, - 7), a = 1, b = \frac{1}{3}

4 x^{2} - 9 y^{2} + 24 x - 36 y - 36 = 0

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

\frac{x ^{2}}{25} - \frac{y ^{2}}{121} = 1

\frac{( x + 4 ) ^{2}}{25} - \frac{( y - 2 ) ^{2}}{4} = 1

x^{2} - y^{2} - 9 = 3

What is (x-9)^2-9(y+7)^2=1 ?
The solution to (x-9)^2-9(y+7)^2=1 is Hyperbola with (h,k)=(9,-7),a=1,b= 1/3