What is 25(x-3)^2-5(y-1)^2=125 ?

The solution to 25(x-3)^2-5(y-1)^2=125 is Hyperbola with (h,k)=(3,1),a=sqrt(5),b=5

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25(x-3)^2-5(y-1)^2=125

25 (x - 3)^{2} - 5 (y - 1)^{2} = 125

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

Solution steps

25 (x - 3)^{2} - 5 (y - 1)^{2} = 125

Rewrite

25 (x - 3)^{2} - 5 (y - 1)^{2} = 125

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

π (a^{2} - b^{2}) = \frac{49 π}{2}

a^{2} - b^{2} = 891

\frac{( x + 2 ) ^{2}}{10} - \frac{( y + 4 ) ^{2}}{25} = 1

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

x^{2} - 4 y^{2} + 16 = 0

What is 25(x-3)^2-5(y-1)^2=125 ?
The solution to 25(x-3)^2-5(y-1)^2=125 is Hyperbola with (h,k)=(3,1),a=sqrt(5),b=5