What is y^2=x^2-5x+4 ?

The solution to y^2=x^2-5x+4 is Hyperbola with (h,k)=(5/2 ,0),a= 3/2 ,b= 3/2

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y^2=x^2-5x+4

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

(h, k) = (\frac{5}{2}, 0), a = \frac{3}{2}, b = \frac{3}{2}

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

\frac{( x - \frac{5}{2} ) ^{2}}{( \frac{3}{2} ) ^{2}} - \frac{( y - 0 ) ^{2}}{( \frac{3}{2} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (\frac{5}{2}, 0), a = \frac{3}{2}, b = \frac{3}{2}

a^{2} - b^{2} = 50

x^{2} - 9 = 2 y^{2}

4 x^{2} - 24 x - 25 y^{2} + 250 y - 489 = 0

\frac{y ^{2}}{1 0 ^{2}} - \frac{x ^{2}}{2 4 ^{2}} = 1

4 x^{2} - y^{2} + 24 x + 40 = 0

What is y^2=x^2-5x+4 ?
The solution to y^2=x^2-5x+4 is Hyperbola with (h,k)=(5/2 ,0),a= 3/2 ,b= 3/2