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

The solution to x^2-y^2+6x+10y=2 is Hyperbola with (h,k)=(-3,5),a=sqrt(14),b=sqrt(14)

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x^2-y^2+6x+10y=2

x^{2} - y^{2} + 6 x + 10 y = 2

(h, k) = (- 3, 5), a = 14, b = 14

Solution steps

x^{2} - y^{2} + 6 x + 10 y = 2

Rewrite

x^{2} - y^{2} + 6 x + 10 y = 2

in the form of a standard hyperbola equation

\frac{( y - 5 ) ^{2}}{( 14 ) ^{2}} - \frac{( x - ( - 3 ) ) ^{2}}{( 14 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- 3, 5), a = 14, b = 14

\frac{( y + 3 ) ^{2}}{16} - \frac{( x + 1 ) ^{2}}{4} = 1

4 y^{2} - 2 x^{2} - 4 y - 15 = 0

\frac{x ^{2}}{2} - \frac{1}{2} = \frac{y ^{2}}{200} - \frac{1}{200}

- y^{2} + 8 z^{2} = - 8

9 x^{2} - 8 y^{2} = 3

What is x^2-y^2+6x+10y=2 ?
The solution to x^2-y^2+6x+10y=2 is Hyperbola with (h,k)=(-3,5),a=sqrt(14),b=sqrt(14)