Sequences & Series
Parabola and inverse trigonometric functions (misplaced question)
nta_pyq_2023_jan
Grade None
Question:
Let $y = f(x)$ represent a parabola with focus $\left(-\dfrac{1}{2}, 0\right)$ and directrix $y = -\dfrac{1}{2}$. Then $S = \left\{x \in \mathbb{R} : \tan^{-1}\left(\sqrt{f(x)}\right) + \sin^{-1}\left(\sqrt{f(x)+1}\right) = \dfrac{\pi}{2}\right\}$:
contains exactly two elements
contains exactly one element
is an infinite set
is an empty set
Step-by-Step Solution
Key Concept: Find the parabola equation from focus and directrix, then determine for which $x$ the inverse trig equation holds.
Answer: (1) contains exactly two elements.
Correct Answer: 1