AP EAMCET · Maths · Application of Derivatives
The angle between the curves \(\mathrm{y}^2=\mathrm{x}\) and \(\mathrm{x}^2=\mathrm{y}\) at the point \((1,1)\) is
- A \(\operatorname{Tan}^{-1}\left(\frac{4}{3}\right)\)
- B \(\operatorname{Tan}^{-1}\left(\frac{3}{4}\right)\)
- C \(90^{\circ}\)
- D \(45^{\circ}\)
Answer & Solution
Correct Answer
(B) \(\operatorname{Tan}^{-1}\left(\frac{3}{4}\right)\)
Step-by-step Solution
Detailed explanation
\(\mathrm{y}^2=\mathrm{x} \implies 2\mathrm{y}\frac{\mathrm{dy}}{\mathrm{dx}} = 1 \implies \mathrm{m}_1 = \frac{1}{2\mathrm{y}}\) \(\mathrm{m}_1 \text{ at } (1,1) = \frac{1}{2(1)} = \frac{1}{2}\)…
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