TechComm Solutions is designing a satellite communication network for a rural mountain region. They need to strategically place satellite dishes to ensure optimal coverage while working within terrain constraints and signal strength requirements. The engineering team must determine exact intersection points where coverage areas meet.

The Network Design Challenge

The engineering team is working with two primary satellite dishes that will provide overlapping coverage:

• Dish A: Creates a circular coverage area described by [latex]x^2 + y^2 = 25[/latex] (radius of 5 km)
• Dish B: Positioned to create coverage following [latex]y = x^2 - 4[/latex] (parabolic pattern)

The team needs to find where these coverage areas intersect to place relay towers at the optimal connection points.