What is 4x^2-5y^2-36y-36=0 ?

The solution to 4x^2-5y^2-36y-36=0 is Hyperbola with (h,k)=(0,-18/5),a= 12/5 ,b= 6/(sqrt(5))

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4x^2-5y^2-36y-36=0

4 x^{2} - 5 y^{2} - 36 y - 36 = 0

(h, k) = (0, - \frac{18}{5}), a = \frac{12}{5}, b = \frac{6}{5}

Solution steps

4 x^{2} - 5 y^{2} - 36 y - 36 = 0

Rewrite

4 x^{2} - 5 y^{2} - 36 y - 36 = 0

in the form of a standard hyperbola equation

\frac{( y - ( - \frac{18}{5} ) ) ^{2}}{( \frac{12}{5} ) ^{2}} - \frac{( x - 0 ) ^{2}}{( \frac{6}{5} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, - \frac{18}{5}), a = \frac{12}{5}, b = \frac{6}{5}

y^{2} - 1 = 16 (x^{2} - 1)

5 x^{2} - 4 y^{2} - 18 y + 9 = 0

\frac{( x + 3 ) ^{2}}{4} - \frac{( y + 1 ) ^{2}}{9} = 1

\frac{( y + 3 ) ^{2}}{81} - \frac{( x + 3 ) ^{2}}{16} = 1

(x - 4)^{2} - (y - 4)^{2} \leq 9

What is 4x^2-5y^2-36y-36=0 ?
The solution to 4x^2-5y^2-36y-36=0 is Hyperbola with (h,k)=(0,-18/5),a= 12/5 ,b= 6/(sqrt(5))