Question

Find the acute angles between the curves y = |x² – 1| and y = |x² – 3| at their points of intersection.

Answer 1

Given curves are y = |x² – 1| and y = |x² – 3|

The points of intersection are (±√ 2 , 1).

Since the curves are symmetrical about y - axis,

so the angle of intersection at (√2 , 1) = the angle of intersection at (–√2 , 1)

At (√2 , 1), m₁ = 2x = 2√2

and m₂ = – 2x = – 2√2

Let θ be the angle between them

Then tanθ = |4√2/(1 – 8)| = 4√2/7

⇒ θ = tan^–1(4√2/7)