JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
Let \(y=f(x)\) represent a parabola with focus \(\left(-\frac{1}{2}, 0\right)\) and directrix \(y =-\frac{1}{2}\). Then \(S=\left\{x \in R : \tan ^{-1}\left(\sqrt{f(x)}+\sin ^{-1}(\sqrt{f(x)+1})\right)=\frac{\pi}{2}\right\}:\)
- A contains exactly two elements
- B contains exactly one element
- C is an infinite set
- D is an empty set
Answer & Solution
Correct Answer
(A) contains exactly two elements
Step-by-step Solution
Detailed explanation
\(\left( x +\frac{1}{2}\right)^2=\left( y +\frac{1}{4}\right)\) \(y=\left(x^2+x\right)\) \(\tan ^{-1} \sqrt{ x ( x +1)}+\sin ^{-1} \sqrt{ x ^2+ x +1}=\pi / 2\) \(0 \leq x ^2+ x +1 \leq 1\) \(x^2+x \leq 0\) \(\text { Also } x^2+x \geq 0\) \(\therefore x^2+x=0 \Rightarrow x=0,-1\)…
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