Question
Question: The point (a, 2a) is an interior point of the region bounded by the parabola y<sup>2</sup> = 16x and...
The point (a, 2a) is an interior point of the region bounded by the parabola y2 = 16x and the double ordinate through the focus. Then a belongs to the open interval
A
a< 4
B
0 < a < 4
C
0 < a < 2
D
a > 4
Answer
0 < a < 2
Explanation
Solution
The point (a, 2a) is in the shaded portion ie., inside the parabola y2 = 16x and left side of the line x = 4.
ie. 4a2 – 16a < 0 and 2a – 4 < 0
⇒ a(a – 4) < 0 and a < 2
⇒ 0 < a < 2