What is 6x^2-5y^2+36x+20y-16=0 ?

The solution to 6x^2-5y^2+36x+20y-16=0 is Hyperbola with (h,k)=(-3,2),a= 5/(sqrt(3)),b=sqrt(10)

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6x^2-5y^2+36x+20y-16=0

6 x^{2} - 5 y^{2} + 36 x + 20 y - 16 = 0

(h, k) = (- 3, 2), a = \frac{5}{3}, b = 10

Solution steps

6 x^{2} - 5 y^{2} + 36 x + 20 y - 16 = 0

Rewrite

6 x^{2} - 5 y^{2} + 36 x + 20 y - 16 = 0

in the form of a standard hyperbola equation

\frac{( x - ( - 3 ) ) ^{2}}{( \frac{5}{3} ) ^{2}} - \frac{( y - 2 ) ^{2}}{( 10 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- 3, 2), a = \frac{5}{3}, b = 10

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

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

\frac{x ^{2}}{64} - \frac{y ^{2}}{16} = 1

\frac{( x - 3 ) ^{2}}{4} - \frac{y ^{2}}{25} = 1

x^{2} - 4 y^{2} - 4 > 0

What is 6x^2-5y^2+36x+20y-16=0 ?
The solution to 6x^2-5y^2+36x+20y-16=0 is Hyperbola with (h,k)=(-3,2),a= 5/(sqrt(3)),b=sqrt(10)