What is 5y^2-6x-3x^2-10y-13=0 ?

The solution to 5y^2-6x-3x^2-10y-13=0 is Hyperbola with (h,k)=(-1,1),a=sqrt(3),b=sqrt(5)

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5y^2-6x-3x^2-10y-13=0

5 y^{2} - 6 x - 3 x^{2} - 10 y - 13 = 0

(h, k) = (- 1, 1), a = 3, b = 5

Solution steps

5 y^{2} - 6 x - 3 x^{2} - 10 y - 13 = 0

Rewrite

5 y^{2} - 6 x - 3 x^{2} - 10 y - 13 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (- 1, 1), a = 3, b = 5

[f (x)]^{2} = 5 x^{2} - x + 3

2 y^{2} + \frac{10}{2} x^{2} - 8 + 1 = 3 y^{2} - 4

3 x^{2} - 4 y^{2} = 36

13 x^{2} - 14 x - 26 = 13 y^{2} + 18 y - 7

19 x^{2} - 9 y^{2} - 64 x - 18 y + 199 = 0

What is 5y^2-6x-3x^2-10y-13=0 ?
The solution to 5y^2-6x-3x^2-10y-13=0 is Hyperbola with (h,k)=(-1,1),a=sqrt(3),b=sqrt(5)