Question

The range of a radio station is bounded by the circle with equation x2 + y2 = 2025. A stretch of highway near the station is modeled by the equation y - 15 = (1/20)x2. At what points does a car on the highway enter or exit the broadcast range of the station?

Answer 1

you need to solve this system for a and y:-

x^2 + y^2 = 2025
y = (1/20)x^2 + 15
substituting:-

x^2 + ( 0.05x^2 + 15)^2 = 2025
x^2 + 0.0025x^4 + 1.5x^2 + 225 = 2025
0.0025x^4 + 2.5x^2 - 1800 = 0
solving this gives x^2 = 484.88

so x = +/- sqrt 484.88

find the y coordidnates by substituting in the first equation