What is 33(x-2)^2-16(y-5)^2=528 ?

The solution to 33(x-2)^2-16(y-5)^2=528 is Hyperbola with (h,k)=(2,5),a=4,b=sqrt(33)

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33(x-2)^2-16(y-5)^2=528

33 (x - 2)^{2} - 16 (y - 5)^{2} = 528

(h, k) = (2, 5), a = 4, b = 33

Solution steps

33 (x - 2)^{2} - 16 (y - 5)^{2} = 528

Rewrite

33 (x - 2)^{2} - 16 (y - 5)^{2} = 528

in the form of a standard hyperbola equation

\frac{( x - 2 ) ^{2}}{4 ^{2}} - \frac{( y - 5 ) ^{2}}{( 33 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (2, 5), a = 4, b = 33

4 x^{2} - 5 y^{2} - x + 16 y - 1 = 0

9 x^{2} - 16 y^{2} + 54 x - 32 y - 79 = 0

x, x = 3.4 h (x)^{2} - 8 h - 4 x^{2} + 8 x

x^{2} - 3 y^{2} - 3 x = y + 5

x^{2} - 92 y^{2} = 1

What is 33(x-2)^2-16(y-5)^2=528 ?
The solution to 33(x-2)^2-16(y-5)^2=528 is Hyperbola with (h,k)=(2,5),a=4,b=sqrt(33)