1. The problem is to compare the ellipse equation $$\frac{x^2}{64} + \frac{y^2}{100} = 1$$ with the standard form of an ellipse centered at the origin: $$\frac{x^2}{b^2} + \frac{y^2}{a^2} = 1$$ and find the values of $a$ and $b$. 2. In the standard form, $a^2$ is the denominator under $y^2$ and $b^2$ is the denominator under $x^2$. Also, $a$ is the length of the semi-major axis and $b$ is the length of the semi-minor axis. The larger denominator corresponds to $a^2$. 3. Comparing the given equation, we see: $$b^2 = 64$$ $$a^2 = 100$$ 4. To find $a$ and $b$, take the square root of each: $$a = \sqrt{100} = 10$$ $$b = \sqrt{64} = 8$$ 5. Therefore, the ellipse has semi-major axis length $a = 10$ and semi-minor axis length $b = 8$. Final answers: $$a^2 = 100 \implies a = 10$$ $$b^2 = 64 \implies b = 8$$