What is (x-4)^2-9(y+7)^2=1 ?

The solution to (x-4)^2-9(y+7)^2=1 is Hyperbola with (h,k)=(4,-7),a=1,b= 1/3

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(x-4)^2-9(y+7)^2=1

(x - 4)^{2} - 9 (y + 7)^{2} = 1

(h, k) = (4, - 7), a = 1, b = \frac{1}{3}

Solution steps

(x - 4)^{2} - 9 (y + 7)^{2} = 1

Rewrite

(x - 4)^{2} - 9 (y + 7)^{2} = 1

in the form of a standard hyperbola equation

\frac{( x - 4 ) ^{2}}{1 ^{2}} - \frac{( y - ( - 7 ) ) ^{2}}{( \frac{1}{3} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (4, - 7), a = 1, b = \frac{1}{3}

16 x^{2} - 25 y^{2} + 96 x + 544 = 0

9 x^{2} - 4 y^{2} - 54 x + 8 y + 113 = 0

25 x^{2} + 10922 x - 25 y^{2} - y^{2} = 1439

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

9 x^{2} - 4 y^{2} + 54 x + 8 y + 78 = 0

What is (x-4)^2-9(y+7)^2=1 ?
The solution to (x-4)^2-9(y+7)^2=1 is Hyperbola with (h,k)=(4,-7),a=1,b= 1/3