What is (2x-1)^2+(3x-1)^2=y^2 ?

The solution to (2x-1)^2+(3x-1)^2=y^2 is Hyperbola with (h,k)=(5/13 ,0),a=sqrt(1/13),b= 1/13

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(2x-1)^2+(3x-1)^2=y^2

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

(h, k) = (\frac{5}{13}, 0), a = \frac{1}{13}, b = \frac{1}{13}

Solution steps

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

Rewrite

(2 x - 1)^{2} + (3 x - 1)^{2} - y^{2} = 0

in the form of a standard hyperbola equation

\frac{( y - 0 ) ^{2}}{( \frac{1}{13} ) ^{2}} - \frac{( x - \frac{5}{13} ) ^{2}}{( \frac{1}{13} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (\frac{5}{13}, 0), a = \frac{1}{13}, b = \frac{1}{13}

36 y^{2} - 5 x^{2} = 180

\frac{( x + 1 ) ^{2}}{4} - \frac{( y - 2 ) ^{2}}{16} = 1

\frac{( x - 2 ) ^{2}}{7} - \frac{( y + 1 ) ^{2}}{9} = 1

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

8 y^{2} - x^{2} - 16 y + 8 x - 32 = 0

What is (2x-1)^2+(3x-1)^2=y^2 ?
The solution to (2x-1)^2+(3x-1)^2=y^2 is Hyperbola with (h,k)=(5/13 ,0),a=sqrt(1/13),b= 1/13