Question

The point (a, 2a) is an interior point of the region bounded by the parabola $y^{2} = 16x$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 1

Answer: (B)

0 < a < 4

Answer 2

(a, 2a) is an interior point of $y^{2} - 16x = 0$

if $(2a)^{2} - 16a < 0,$ i.e. $a^{2} - 4a < 0$

V (0,0) and (a, 2a) are on the same side

Of $x - 4 = 0$, So, a -4 < 0, i.e., $a < 4$

Now, $a^{2} - 4a < 0$ ⇒ $0 < a < 4$