TS EAMCET · Maths · Application of Derivatives
The length of the normal drawn at \(t=\frac{\pi}{4}\) on the curve \(x=2(\cos 2 t+t \sin 2 t), y=4(\sin 2 t+t \cos 2 t)\) is
- A \(\frac{4}{\pi} \sqrt{1+\pi^2}\)
- B \(4 \sqrt{1+\pi^2}\)
- C \(4 \pi\)
- D \(\frac{4}{\pi}\)
Answer & Solution
Correct Answer
(B) \(4 \sqrt{1+\pi^2}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \quad x=2 \times \frac{\pi}{4} \times 1=1 \text { at } t=\frac{\pi}{4} \\ & \text { At } t=\frac{\pi}{4} \Rightarrow y=4 ; \frac{d x}{d t}=2[-2 \sin 2 t+\sin 2 t+2 t \cos 2 t] \\ & \text { At } t=\frac{\pi}{4} \Rightarrow \frac{d x}{d t}=2 \times(-2+1)=-2 \\ &…
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