What is 4y^2-9x^2+40y-540x-8036=0 ?

The solution to 4y^2-9x^2+40y-540x-8036=0 is Hyperbola with (h,k)=(-30,-5),a=3,b=2

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4y^2-9x^2+40y-540x-8036=0

4 y^{2} - 9 x^{2} + 40 y - 540 x - 8036 = 0

(h, k) = (- 30, - 5), a = 3, b = 2

Solution steps

4 y^{2} - 9 x^{2} + 40 y - 540 x - 8036 = 0

Rewrite

4 y^{2} - 9 x^{2} + 40 y - 540 x - 8036 = 0

in the form of a standard hyperbola equation

\frac{( y - ( - 5 ) ) ^{2}}{3 ^{2}} - \frac{( x - ( - 30 ) ) ^{2}}{2 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- 30, - 5), a = 3, b = 2

16 x^{2} - 25 y^{2} - 400 = 0

x^{2} - 25 y^{2} - 14 x + 100 y - 76 = 0

- x^{2} + 4 y^{2} - 1 = 0

\frac{( y - 4 ) ^{2}}{36} - x^{2} = 1

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

What is 4y^2-9x^2+40y-540x-8036=0 ?
The solution to 4y^2-9x^2+40y-540x-8036=0 is Hyperbola with (h,k)=(-30,-5),a=3,b=2