What is y^2=5x^2-7x+2 ?

The solution to y^2=5x^2-7x+2 is Hyperbola with (h,k)=(7/10 ,0),a= 3/10 ,b= 3/(2sqrt(5))

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y^2=5x^2-7x+2

y^{2} = 5 x^{2} - 7 x + 2

(h, k) = (\frac{7}{10}, 0), a = \frac{3}{10}, b = \frac{3}{2 5}

Solution steps

y^{2} = 5 x^{2} - 7 x + 2

Rewrite

y^{2} = 5 x^{2} - 7 x + 2

in the form of a standard hyperbola equation

\frac{( x - \frac{7}{10} ) ^{2}}{( \frac{3}{10} ) ^{2}} - \frac{( y - 0 ) ^{2}}{( \frac{3}{2 5} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (\frac{7}{10}, 0), a = \frac{3}{10}, b = \frac{3}{2 5}

\frac{( x - 2 ) ^{2}}{1} - \frac{( y + 3 ) ^{2}}{9} = 1

\frac{( x - 3 ) ^{2}}{49} - \frac{( y + 2 ) ^{2}}{16} = 1

3 x^{2} - y^{2} - 2 x + 39 = 0

3 x^{2} - 4 y^{2} + y = 9

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

What is y^2=5x^2-7x+2 ?
The solution to y^2=5x^2-7x+2 is Hyperbola with (h,k)=(7/10 ,0),a= 3/10 ,b= 3/(2sqrt(5))