What is x^2+10x+25-y^2-6y+9=36 ?

The solution to x^2+10x+25-y^2-6y+9=36 is Hyperbola with (h,k)=(-5,-3),a=3sqrt(2),b=3sqrt(2)

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x^2+10x+25-y^2-6y+9=36

x^{2} + 10 x + 25 - y^{2} - 6 y + 9 = 36

(h, k) = (- 5, - 3), a = 32, b = 32

Solution steps

x^{2} + 10 x + 25 - y^{2} - 6 y + 9 = 36

Rewrite

x^{2} + 10 x + 25 - y^{2} - 6 y + 9 = 36

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (- 5, - 3), a = 32, b = 32

y^{2} = x^{2} + 3

\frac{x ^{2}}{64} - \frac{y ^{2}}{9} = 1

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

36 y^{2} - x^{2} = 9

2 x + 5 y = \frac{21}{2 x - 5 y - 11}

What is x^2+10x+25-y^2-6y+9=36 ?
The solution to x^2+10x+25-y^2-6y+9=36 is Hyperbola with (h,k)=(-5,-3),a=3sqrt(2),b=3sqrt(2)