What is a^2-b^2=2018-2a ?

The solution to a^2-b^2=2018-2a is Hyperbola with (h,k)=(-1,0),a=sqrt(2019),b=sqrt(2019)

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a^2-b^2=2018-2a

a^{2} - b^{2} = 2018 - 2 a

(h, k) = (- 1, 0), a = 2019, b = 2019

Solution steps

a^{2} - b^{2} = 2018 - 2 a

Rewrite

a^{2} - b^{2} = 2018 - 2 a

in the form of a standard hyperbola equation

\frac{( a - ( - 1 ) ) ^{2}}{( 2019 ) ^{2}} - \frac{( b - 0 ) ^{2}}{( 2019 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- 1, 0), a = 2019, b = 2019

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

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

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

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

\frac{x ^{2}}{2 + y ^{2}} = 1

What is a^2-b^2=2018-2a ?
The solution to a^2-b^2=2018-2a is Hyperbola with (h,k)=(-1,0),a=sqrt(2019),b=sqrt(2019)