What is p^2+2021=q^2 ?

The solution to p^2+2021=q^2 is Hyperbola with (h,k)=(0,0),a=sqrt(2021),b=sqrt(2021)

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p^2+2021=q^2

p^{2} + 2021 = q^{2}

(h, k) = (0, 0), a = 2021, b = 2021

Solution steps

p^{2} + 2021 = q^{2}

Rewrite

p^{2} + 2021 = q^{2}

in the form of a standard hyperbola equation

\frac{( q - 0 ) ^{2}}{( 2021 ) ^{2}} - \frac{( p - 0 ) ^{2}}{( 2021 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, 0), a = 2021, b = 2021

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

x^{2} - 9 y^{2} + 4 x + 18 y - 149 = 3

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

4 x^{2} - 5 y^{2} + 32 x + 30 y = 1

3 y^{2} - 5 x^{2} + 18 y - 40 x - 533 = 0

What is p^2+2021=q^2 ?
The solution to p^2+2021=q^2 is Hyperbola with (h,k)=(0,0),a=sqrt(2021),b=sqrt(2021)