a^2 − b^2 = 2024.
You asked:
Investigate the equation: \({a}^{2} - {b}^{2} = 2024\).
MathBot Answer:
The graph of the equation \({a}^{2} - {b}^{2} = 2024\) is a hyperbola.
The coordinates of its foci are: \(\left(4 \sqrt{253}, 0\right)\) and \(\left(- 4 \sqrt{253}, 0\right)\).
The coordinates of its vertices are: \(\left(2 \sqrt{506}, 0\right)\) and \(\left(- 2 \sqrt{506}, 0\right)\).
The asymptotes have equations: \(4 \sqrt{506} a + 4 \sqrt{506} b = 0\) and \(4 \sqrt{506} a - 4 \sqrt{506} b = 0\).