What is 5x^2-5y^2+20x-60y=185 ?

The solution to 5x^2-5y^2+20x-60y=185 is Hyperbola with (h,k)=(-2,-6),a=sqrt(5),b=sqrt(5)

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5x^2-5y^2+20x-60y=185

5 x^{2} - 5 y^{2} + 20 x - 60 y = 185

(h, k) = (- 2, - 6), a = 5, b = 5

Solution steps

5 x^{2} - 5 y^{2} + 20 x - 60 y = 185

Rewrite

5 x^{2} - 5 y^{2} + 20 x - 60 y = 185

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (- 2, - 6), a = 5, b = 5

\frac{x ^{2}}{9} - \frac{y ^{2}}{1} = 1

x^{2} - 5 y^{2} = 3 y

\frac{y ^{2}}{81} - \frac{x ^{2}}{25} = 1

x^{2} - 3 y^{2} + 2 x + 6 y - 1 = 0

x^{2} - y^{2} - 2 x - 4 y = - 4

What is 5x^2-5y^2+20x-60y=185 ?
The solution to 5x^2-5y^2+20x-60y=185 is Hyperbola with (h,k)=(-2,-6),a=sqrt(5),b=sqrt(5)