What is (x-2)^2-(y+5)^2=18 ?

The solution to (x-2)^2-(y+5)^2=18 is Hyperbola with (h,k)=(2,-5),a=3sqrt(2),b=3sqrt(2)

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(x-2)^2-(y+5)^2=18

(x - 2)^{2} - (y + 5)^{2} = 18

(h, k) = (2, - 5), a = 32, b = 32

Solution steps

(x - 2)^{2} - (y + 5)^{2} = 18

Rewrite

(x - 2)^{2} - (y + 5)^{2} = 18

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (2, - 5), a = 32, b = 32

\frac{4 y ^{2}}{9} - \frac{4 x ^{2}}{27} = 1

2 x^{2} - 3 y^{2} + 8 x + 6 y - 115 = 0

x^{2} - 4 y^{2} = 5

a^{2} - 4 b^{2} = 15

9 x^{2} - 4 y^{2} - 18 x + 8 y + 10 = 0

What is (x-2)^2-(y+5)^2=18 ?
The solution to (x-2)^2-(y+5)^2=18 is Hyperbola with (h,k)=(2,-5),a=3sqrt(2),b=3sqrt(2)