What is 4y^2-x^2+40y-4x+60=0 ?

The solution to 4y^2-x^2+40y-4x+60=0 is Hyperbola with (h,k)=(-2,-5),a=3,b=6

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4y^2-x^2+40y-4x+60=0

4 y^{2} - x^{2} + 40 y - 4 x + 60 = 0

(h, k) = (- 2, - 5), a = 3, b = 6

Solution steps

4 y^{2} - x^{2} + 40 y - 4 x + 60 = 0

Rewrite

4 y^{2} - x^{2} + 40 y - 4 x + 60 = 0

in the form of a standard hyperbola equation

\frac{( y - ( - 5 ) ) ^{2}}{3 ^{2}} - \frac{( x - ( - 2 ) ) ^{2}}{6 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- 2, - 5), a = 3, b = 6

\frac{( x + 5 ) ^{2}}{4} - \frac{y ^{2}}{4} = 1

9 x^{2} - 4 y^{2} - 18 x - 16 y + 29 = 0

y^{2} - 25 x^{2} + 8 y - 9 = 0

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

49 x^{2} - 36 y^{2} = 1764

What is 4y^2-x^2+40y-4x+60=0 ?
The solution to 4y^2-x^2+40y-4x+60=0 is Hyperbola with (h,k)=(-2,-5),a=3,b=6