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AP EAMCET · Maths · Application of Derivatives

The angle between the tangents drawn at \((0,0)\) to the curves \(y^3-x^2 y+5 y-2 x=0\) and \(x^4-x^3 y^2+5 x+2 y=0\) is

  1. A \(\frac{\pi}{6}\)
  2. B \(\frac{\pi}{4}\)
  3. C \(\frac{\pi}{3}\)
  4. D \(\frac{\pi}{2}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{\pi}{2}\)

Step-by-step Solution

Detailed explanation

\begin{aligned} & \text { } y^3-x^2 y+5 y-2 x=0 \\ & \Rightarrow \quad 3 y^2 \frac{d y}{d x}-x^2 \frac{d y}{d x}-2 x y+5 \frac{d y}{d x}-2=0 \\ & \Rightarrow \quad \frac{d y}{d x}=\frac{2 x y+2}{3 y^2-x^2+5} \\ & \quad m_1=\left.\frac{d y}{d x}\right|_{(0,0)}=\frac{2}{5}…