Equation of parabola with focus (−21,0) and directrix y=−21 is:
(x+21)2=(y+41)
⇒y=(x2+x)
Put f(x)=y=x+x2 in S,
tan−1x(x+1)+sin−1x2+x+1=2π
⇒0≤x2+x+1≤1
⇒x2+x≤0…(1)
Also,
x2+x≥0…(2)
By (1)&(2), we have
x2+x=0⇒x=0,−1
S contains 2 element.
Let y=f(x) represent a parabola with focus (−21,0) and directrix y=−21. Then S=x∈R:tan−1(f(x)+sin−1(f(x)+1))=2π:
Held on 31 Jan 2023 · Verified 6 Jul 2026.
contains exactly two elements
contains exactly one element
is an infinite set
is an empty set
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