1. Understanding the Problem and Key Concept

The problem asks us to find the angle of intersection between two given curves:

• Curve 1 (Ellipse): $C_1: \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$
• Curve 2 (Circle): $C_2: x^2 + y^2 = ab$ We are given that $a > b$.

Key Concept: The angle between two intersecting curves at a point $(x_0, y_0)$ is defined as the angle between their respective tangent lines at that point. If $m_1$ and $m_2$ are the slopes of the tangent lines to the two curves at their