TS EAMCET · Maths · Application of Derivatives
If at any point \(\left(x_1, y_1\right)\) on the curve \(y=f(x)\) the lengths of the subtangent and subnormal are equal, then the length of the tangent drawn to that curve at that point is
- A \(2\left|y_1\right|\)
- B \(\sqrt{2}\left|y_1\right|\)
- C \(\sqrt{5}\left|y_1\right|\)
- D \(\sqrt{2}\left|\frac{y_1}{x_1}\right|\)
Answer & Solution
Correct Answer
(B) \(\sqrt{2}\left|y_1\right|\)
Step-by-step Solution
Detailed explanation
We have, Length of subtangent \(=\) Length of subnormal \(\therefore \quad y_1 \frac{d x}{d y}=y_1 \frac{d y}{d x}\) \(\Rightarrow \quad \frac{d y}{d x}= \pm 1\) Length of tangent \(=\left|y_1 \sqrt{1+\left(\frac{d x}{d y}\right)^2}\right|\) Length of tangent…
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