What is x^2+12x-y^2+10y=12 ?

The solution to x^2+12x-y^2+10y=12 is Hyperbola with (h,k)=(-6,5),a=sqrt(23),b=sqrt(23)

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x^2+12x-y^2+10y=12

x^{2} + 12 x - y^{2} + 10 y = 12

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

Solution steps

x^{2} + 12 x - y^{2} + 10 y = 12

Rewrite

x^{2} + 12 x - y^{2} + 10 y = 12

in the form of a standard hyperbola equation

\frac{( x - ( - 6 ) ) ^{2}}{( 23 ) ^{2}} - \frac{( y - 5 ) ^{2}}{( 23 ) ^{2}} = 1

Therefore Hyperbola properties are:

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

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

y^{2} - 4 y = 3 x^{2} - 10 x

(\frac{a + b}{100}) \cdot (a - b) = \frac{1}{25}

x^{2} + 3 x - 2 y^{2} + y - 23 = 0

\frac{( y - 8 ) ^{2}}{4} - \frac{( x - 5 ) ^{2}}{9} = 1

What is x^2+12x-y^2+10y=12 ?
The solution to x^2+12x-y^2+10y=12 is Hyperbola with (h,k)=(-6,5),a=sqrt(23),b=sqrt(23)