What is (u-7)^2=2y^2-18y+28 ?

The solution to (u-7)^2=2y^2-18y+28 is Hyperbola with (h,k)=(7, 9/2),a= 5/2 ,b= 5/(sqrt(2))

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(u-7)^2=2y^2-18y+28

(u - 7)^{2} = 2 y^{2} - 18 y + 28

(h, k) = (7, \frac{9}{2}), a = \frac{5}{2}, b = \frac{5}{2}

Solution steps

(u - 7)^{2} = 2 y^{2} - 18 y + 28

Rewrite

(u - 7)^{2} - 2 y^{2} + 18 y - 28 = 0

in the form of a standard hyperbola equation

\frac{( y - \frac{9}{2} ) ^{2}}{( \frac{5}{2} ) ^{2}} - \frac{( u - 7 ) ^{2}}{( \frac{5}{2} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (7, \frac{9}{2}), a = \frac{5}{2}, b = \frac{5}{2}

2 (x^{2} - 10 x) - 9 (y^{2} - 8 y) = - 16

\frac{x ^{2}}{36} - \frac{y ^{2}}{100} = 1

\frac{( x - 5 ) ^{2}}{4} - \frac{( y - 3 ) ^{2}}{4} = 1

x^{2} - 4 y^{2} + 2 x - 16 y + 13 = 0

(x - 1)^{2} - (y - 10)^{2} = - 40

What is (u-7)^2=2y^2-18y+28 ?
The solution to (u-7)^2=2y^2-18y+28 is Hyperbola with (h,k)=(7, 9/2),a= 5/2 ,b= 5/(sqrt(2))