Problema Solution
A radio tower is located on a coordinate system measured in miles. The range of a signal in a particular direction is modeled by a quadratic function where the boundary of the signal starts at the vertex at (4, 2). It passes through the point (5, 4). A linear road connects points (–3, 7) and (8, 2). Which system of equations can be used to determine whether the road intersects the boundary of the tower’s signal?
Answer provided by our tutors
The range of the signal is a circle with center (4, 2) and radii r^2 = (5 - 4)^2 + (4 - 2)^2 or r^2 = 5:
(x - 4)^2 + (y - 2)^2 = 5
The equation of a line trough (–3, 7) and (8, 2) is:
y - 2 = (x - 8)(7 - 2)/(-3 - 8)
y - 2 = - (5/11)x + (40/11)
y = -(5/11)x + (40/11)+2
y = -(5/11)x + (62/11)
The system of equations is:
(x - 4)^2 + (y - 2)^2 = 5
y = -(5/11)x + (62/11)
We can conclude that the road intersects the boundary of the towers signal.
