What is 46^2x^2=40^2y^2+1600 ?

The solution to 46^2x^2=40^2y^2+1600 is Hyperbola with (h,k)=(0,0),a= 20/23 ,b=1

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46^2x^2=40^2y^2+1600

4 6^{2} x^{2} = 4 0^{2} y^{2} + 1600

(h, k) = (0, 0), a = \frac{20}{23}, b = 1

Solution steps

4 6^{2} x^{2} = 4 0^{2} y^{2} + 1600

Rewrite

4 6^{2} x^{2} = 4 0^{2} y^{2} + 1600

in the form of a standard hyperbola equation

\frac{( x - 0 ) ^{2}}{( \frac{20}{23} ) ^{2}} - \frac{( y - 0 ) ^{2}}{1 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, 0), a = \frac{20}{23}, b = 1

4 x^{2} - 45 y^{2} - 180 = 0

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

(\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

What is 46^2x^2=40^2y^2+1600 ?
The solution to 46^2x^2=40^2y^2+1600 is Hyperbola with (h,k)=(0,0),a= 20/23 ,b=1