What is 36(y+4)^2-16(x-3)^2=576 ?

The solution to 36(y+4)^2-16(x-3)^2=576 is Hyperbola with (h,k)=(3,-4),a=4,b=6

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36(y+4)^2-16(x-3)^2=576

36 (y + 4)^{2} - 16 (x - 3)^{2} = 576

(h, k) = (3, - 4), a = 4, b = 6

Solution steps

36 (y + 4)^{2} - 16 (x - 3)^{2} = 576

Rewrite

36 (y + 4)^{2} - 16 (x - 3)^{2} = 576

in the form of a standard hyperbola equation

\frac{( y - ( - 4 ) ) ^{2}}{4 ^{2}} - \frac{( x - 3 ) ^{2}}{6 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (3, - 4), a = 4, b = 6

(x - 2)^{2} - (y + 3)^{2} = 12

4 x^{2} - y^{2} + 12 x + 5 = 0

y^{2} - x^{2} = \frac{1}{25}

x^{2} - 2 y^{2} - 2 x + 8 y + 5 = 0

12 x^{2} - 4 y^{2} = 96

What is 36(y+4)^2-16(x-3)^2=576 ?
The solution to 36(y+4)^2-16(x-3)^2=576 is Hyperbola with (h,k)=(3,-4),a=4,b=6