Question

Franco is adjusting a satellite because he finds it is not focusing the incoming radio waves perfectly. The shape of his satellite can be modeled by mc024-1.jpg, where x and y are modeled in inches. He realizes that the static is a result of the feed antenna shifting slightly off the focus point. What is the focus point of the satellite?
(2, –3)
(–1.25, –3)
(3, 2.75)
(3, 4.75)

Answer 1

Focus = (3, 2.75).

Reason: The parabola can be written (x − 3)^2 = 16(y + 1.25), so its vertex is (3, −1.25) and 4p = 16 ⇒ p = 4. Since it opens upward the focus is (3, −1.25 + 4) = (3, 2.75).