What is 12(y-5)^2-30(x+2)^2=360 ?

The solution to 12(y-5)^2-30(x+2)^2=360 is Hyperbola with (h,k)=(-2,5),a=sqrt(30),b=2sqrt(3)

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12(y-5)^2-30(x+2)^2=360

12 (y - 5)^{2} - 30 (x + 2)^{2} = 360

(h, k) = (- 2, 5), a = 30, b = 23

Solution steps

12 (y - 5)^{2} - 30 (x + 2)^{2} = 360

Rewrite

12 (y - 5)^{2} - 30 (x + 2)^{2} = 360

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (- 2, 5), a = 30, b = 23

3 x^{2} - y^{2} + 30 x + 78 = 0

9 x^{2} - y^{2} - 72 x + 8 y + 119 = 0

9 x^{2} - 4 y^{2} + 18 x - 27 = 0

4 x^{2} - y^{2} = 64

y^{2} - 16 x^{2} = 16

What is 12(y-5)^2-30(x+2)^2=360 ?
The solution to 12(y-5)^2-30(x+2)^2=360 is Hyperbola with (h,k)=(-2,5),a=sqrt(30),b=2sqrt(3)