In: Math
5. A volcano is located at the point (1, 3). Scientists have determined that a possible eruption of this volcano would affect the area within the radius of 4 miles around the volcano.
(a) Two locations are being considered for a new housing estate: the point (−1, −2) and the point (−1, 6). Determine which of those locations is at a safe distance from the volcano. Justify your answer.
(b) Determine the closest point in the direction ~v = [1, 1] from the volcano, that is safe from a possible eruption.