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

The solution to x^2+(y-5)=(y+5)^2 is Hyperbola with (h,k)=(0,-9/2),a=(sqrt(39))/2 ,b=(sqrt(39))/2

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x^2+(y-5)=(y+5)^2

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

(h, k) = (0, - \frac{9}{2}), a = \frac{39}{2}, b = \frac{39}{2}

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

\frac{( x - 0 ) ^{2}}{( \frac{39}{2} ) ^{2}} - \frac{( y - ( - \frac{9}{2} ) ) ^{2}}{( \frac{39}{2} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, - \frac{9}{2}), a = \frac{39}{2}, b = \frac{39}{2}

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

2 x^{2} - 4 y^{2} = 8

3 y^{2} - 2 x^{2} - x + 5 y - 15 = 0

4 x^{2} - 9 y^{2} - 8 x - 36 y - 68 = 0

3 x^{2} - 5 y^{2} + 6 x + 10 y = 32

What is x^2+(y-5)=(y+5)^2 ?
The solution to x^2+(y-5)=(y+5)^2 is Hyperbola with (h,k)=(0,-9/2),a=(sqrt(39))/2 ,b=(sqrt(39))/2