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

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

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

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

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

Solution steps

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

Rewrite

x - \frac{5 x ^{2} - 5 y ^{2}}{2} = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

- 3 x^{2} + 2 y^{2} + 18 x - 20 y + 17 = 0

\frac{x ^{2}}{8 ^{2}} - \frac{y ^{2}}{5 ^{2}} = 1

4 y^{2} - x^{2} + 16 y + 12 = 0

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

- 4 x^{2} + y^{2} - 40 x - 16 = 0

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