129k views
0 votes
When waiting to land, an airplane is traveling above the airport in a holding pattern that can be modeled by the equation 49x2 + 64y2 = 3136, with the air traffic control tower at the origin. Suppose that another plane approaches the airport at the same altitude as the first plane on a path that can be modeled by the equation y - 6 = (1/4)x2. what are the possible points of collision?

User Dilpreet
by
8.0k points

1 Answer

4 votes
49x^2 + 64y^2 = 3136 . . . (1)
y - 6 = (1/4)x^2 . . . (2)

From (2), x^2 = 4(y - 6) = 4y - 24 . . . (3)

Putting (3) into (1) gives
49(4y - 24) + 64y^2 = 3136
196y - 1176 + 64y^2 = 3136
64y^2 + 196y - 4312 = 0
y = 6.819
x = sqrt(4(6.819) - 24)
x = 1.81

The possible point of collision is (1.81, 6.819)
User EddyR
by
7.3k points

Related questions

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories