The acute angles between the curves y = |x 2 – 1| and
y = |x 2 – 3| at their points of intersection is -
Text Solution
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Clearly when x 2 = 2, y = 1 gives the point of intersection. The given equations represent four parabolas y = ± (x 2 – 1) and y = ± (x 2 – 3) which can be traced. The curves y = x 2 – 1 and y = –(x 2 – 3) intersect when 1 < x 2 < 3 or 1 < x < √ 3 or – √ 3 < x < –1
The points of intersections are (± √ 2, 1). At ( √ 2, 1)
m 1 = 2x = 2 √ 2, m 2 = – 2x = –2 √ 2
∴ tan θ = 
= 
, ∴ θ = tan –1 
In a similar manner the acute angles at the other points in same as found above.
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