What is -((x-5)^2)/4+((y+1)^2)/3 =1 ?

The solution to -((x-5)^2)/4+((y+1)^2)/3 =1 is Hyperbola with (h,k)=(5,-1),a=sqrt(3),b=2

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-((x-5)^2)/4+((y+1)^2)/3 =1

- \frac{( x - 5 ) ^{2}}{4} + \frac{( y + 1 ) ^{2}}{3} = 1

(h, k) = (5, - 1), a = 3, b = 2

Solution steps

- \frac{( x - 5 ) ^{2}}{4} + \frac{( y + 1 ) ^{2}}{3} = 1

Rewrite

- \frac{( x - 5 ) ^{2}}{4} + \frac{( y + 1 ) ^{2}}{3} = 1

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (5, - 1), a = 3, b = 2

a^{2} - b^{2} = 997

25 x^{2} - 36 y^{2} = 900

x^{2} - y^{2} + 2 x + 2 y - 16 = 0

x^{2} - y^{2} - 10 x - 10 y - 1 = 0

x^{2} - x - y - 1 = y^{2} - y - x - 3

What is -((x-5)^2)/4+((y+1)^2)/3 =1 ?
The solution to -((x-5)^2)/4+((y+1)^2)/3 =1 is Hyperbola with (h,k)=(5,-1),a=sqrt(3),b=2