Question
Question: If the normal to the parabola y<sup>2</sup> = 4ax at the point (at<sup>2</sup>, 2at) cuts the parabo...
If the normal to the parabola y2 = 4ax at the point (at2, 2at) cuts the parabola again at (aT2, 2aT), then
A
T2≥ 8
B
T ∈ (- ∞, -8) ∪ (8, ∞)
C
–2 ≤ T ≤ 2
D
T2< 8
Answer
T2≥ 8
Explanation
Solution
Equation of normal to the parabola y2 = 4ax at the point (at2, 2at) is y + tx = 2at + at3. . . . .(i)
(i) cuts the parabola again at (aT2, 2aT).
Then, 2aT + t aT2 = 2at +at3
⇒ 2a(T – t) = – at(T2 – t2) ⇒ 2 = – t(T + t) [t ≠ T]
⇒ t2 + tT + 2 = 0.
Since t is real T2 – 4.2.1 ≥ 0 ⇒ T2 ≥ 8