What is ((x-5)^2)/(12)-((y+6)^2)/(17)=1 ?

The solution to ((x-5)^2)/(12)-((y+6)^2)/(17)=1 is Hyperbola with (h,k)=(5,-6),a=2sqrt(3),b=sqrt(17)

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((x-5)^2)/(12)-((y+6)^2)/(17)=1

\frac{( x - 5 ) ^{2}}{12} - \frac{( y + 6 ) ^{2}}{17} = 1

(h, k) = (5, - 6), a = 23, b = 17

Solution steps

\frac{( x - 5 ) ^{2}}{12} - \frac{( y + 6 ) ^{2}}{17} = 1

Rewrite

\frac{( x - 5 ) ^{2}}{12} - \frac{( y + 6 ) ^{2}}{17} = 1

in the form of a standard hyperbola equation

\frac{( x - 5 ) ^{2}}{( 2 3 ) ^{2}} - \frac{( y - ( - 6 ) ) ^{2}}{( 17 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (5, - 6), a = 23, b = 17

- 36 y = x^{2}

5 x^{2} + 7 y^{2} = 35

\frac{( x + 3 ) ^{2}}{25} - \frac{( y - 4 ) ^{2}}{9} = 1

16 x^{2} - 96 x + 144 + 25 y^{2} = 400

x^{2} = 20 y

What is ((x-5)^2)/(12)-((y+6)^2)/(17)=1 ?
The solution to ((x-5)^2)/(12)-((y+6)^2)/(17)=1 is Hyperbola with (h,k)=(5,-6),a=2sqrt(3),b=sqrt(17)