Mathematics - Application of Derivative Question with Solution | TestHub

MathematicsApplication of DerivativeTangents & NormalsMedium2 minQB

MathematicsMediumsingle choice

If the points of contact of tangents to $y = sin x$ , drawn from origin always lie on $\frac{a}{y ^{2}} - \frac{b}{x ^{2}} = c$ , then,

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Solution:

Let $P (h, k)$ be any point on $y = sin x$ $\Rightarrow k = sin h . tangent at P is y - k = cos h (x - h) (0, 0) \Rightarrow - k = cos h (0 - h) \Rightarrow cos h = \frac{k}{h} \Rightarrow sin^{2} h + cos^{2} h = k^{2} + \frac{k ^{2}}{h ^{2}} = 1 \Rightarrow \frac{1}{y ^{2}} - \frac{1}{x ^{2}} = 1 \Rightarrow a = 1, b = 1, c = 1 ∴ a = b = c, which are in AP, GP and HP$

Stream:JEESubject:MathematicsTopic:Application of DerivativeSubtopic:Tangents & Normals

⏱ 2mℹ️ Source: QB

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