What is 5x^2-9y^2+10x-36y-14=0 ?

The solution to 5x^2-9y^2+10x-36y-14=0 is Hyperbola with (h,k)=(-1,-2),a=(sqrt(17))/3 ,b=sqrt(17/5)

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5x^2-9y^2+10x-36y-14=0

5 x^{2} - 9 y^{2} + 10 x - 36 y - 14 = 0

(h, k) = (- 1, - 2), a = \frac{17}{3}, b = \frac{17}{5}

Solution steps

5 x^{2} - 9 y^{2} + 10 x - 36 y - 14 = 0

Rewrite

5 x^{2} - 9 y^{2} + 10 x - 36 y - 14 = 0

in the form of a standard hyperbola equation

\frac{( y - ( - 2 ) ) ^{2}}{( \frac{17}{3} ) ^{2}} - \frac{( x - ( - 1 ) ) ^{2}}{( \frac{17}{5} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- 1, - 2), a = \frac{17}{3}, b = \frac{17}{5}

x^{2} - y^{2} + 2 x + 5 = 0

x^{2} - y^{2} - 2 x - 8 y - 10 = 0

y^{2} = x^{2} + 361

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

\frac{( x + 3 ) ^{2}}{49} - \frac{( y - 1 ) ^{2}}{48} = 1

What is 5x^2-9y^2+10x-36y-14=0 ?
The solution to 5x^2-9y^2+10x-36y-14=0 is Hyperbola with (h,k)=(-1,-2),a=(sqrt(17))/3 ,b=sqrt(17/5)