AP EAMCET · Maths · Application of Derivatives
The acute angle between the tangents drawn at the point of intersection (other than the origin) of the curves \(x^2=4 y\) and \(y^2=4 x\) is
- A \(\tan ^{-1}\left(\frac{1}{2}\right)\)
- B \(\sin ^{-1}\left(\frac{3}{5}\right)\)
- C \(\cos ^{-1}\left(\frac{1}{3}\right)\)
- D \(\tan ^{-1}\left(\frac{2}{3}\right)\)
Answer & Solution
Correct Answer
(B) \(\sin ^{-1}\left(\frac{3}{5}\right)\)
Step-by-step Solution
Detailed explanation
Point of intersection other then origin is \((4,4)\). Now, slope of fangents to curve \((i)\) at \((4,4)\) is \[ m_1=\left.\frac{d y}{d x}\right|_{(4,4)}=\left.\frac{2 x}{4}\right|_{(4,4)}=2 \] and slope of tangent to curve (ii) at \((4,4)\) is…
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