Application of Derivatives
Angle of Intersection
Premium Question
Grade 12
Question:
The acute angle between the curves $y^2 = x$ and $x^2 = y$ at the point $(1, 1)$ is:
(1) $\tan^{-1}\left(\frac{3}{4}\right)$
(2) $\tan^{-1}\left(\frac{4}{3}\right)$
(3) $\frac{\pi}{4}$
(4) $\frac{\pi}{2}$
Step-by-Step Solution
Key Concept: Differentiate both curves implicitly to find their slopes $m_1, m_2$ at $(1, 1)$, then apply $\tan \theta = \left|\frac{m_1 - m_2}{1 + m_1m_2}\right|$.
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Correct Answer: (1)