What is 36x^{(2)}-16y^{(2)}-288x+160y-400=0 ?

The solution to 36x^{(2)}-16y^{(2)}-288x+160y-400=0 is Hyperbola with (h,k)=(4,5),a=4,b=6

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36x^{(2)}-16y^{(2)}-288x+160y-400=0

36 x^{(2)} - 16 y^{(2)} - 288 x + 160 y - 400 = 0

(h, k) = (4, 5), a = 4, b = 6

Solution steps

36 x^{2} - 16 y^{2} - 288 x + 160 y - 400 = 0

Rewrite

36 x^{2} - 16 y^{2} - 288 x + 160 y - 400 = 0

in the form of a standard hyperbola equation

\frac{( x - 4 ) ^{2}}{4 ^{2}} - \frac{( y - 5 ) ^{2}}{6 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (4, 5), a = 4, b = 6

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

(x - y) (x + y - 1) = 2018

\frac{x ^{2}}{\frac{324}{9}} - \frac{y ^{2}}{\frac{324}{36}} = 1

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

3 y^{2} - 3 x^{2} + 5 x + 10 y = 5 x^{2} + 1

What is 36x^{(2)}-16y^{(2)}-288x+160y-400=0 ?
The solution to 36x^{(2)}-16y^{(2)}-288x+160y-400=0 is Hyperbola with (h,k)=(4,5),a=4,b=6