What is 20(x-y)=5x^2-4y^2 ?

The solution to 20(x-y)=5x^2-4y^2 is Hyperbola with (h,k)=(2, 5/2),a=(sqrt(5))/2 ,b=1

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20(x-y)=5x^2-4y^2

20 (x - y) = 5 x^{2} - 4 y^{2}

(h, k) = (2, \frac{5}{2}), a = \frac{5}{2}, b = 1

Solution steps

20 (x - y) = 5 x^{2} - 4 y^{2}

Rewrite

20 (x - y) - 5 x^{2} + 4 y^{2} = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (2, \frac{5}{2}), a = \frac{5}{2}, b = 1

\frac{y ^{2}}{5} - \frac{x ^{2}}{25} = 1

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

36 x^{2} - 9 y^{2} + 216 x + 36 y = - 207

- 4 x^{2} + y^{2} + 8 x - 20 = 0

\frac{( y - 7 ) ^{2}}{32} - \frac{( x - 1 ) ^{2}}{64} = 1

What is 20(x-y)=5x^2-4y^2 ?
The solution to 20(x-y)=5x^2-4y^2 is Hyperbola with (h,k)=(2, 5/2),a=(sqrt(5))/2 ,b=1