Mathematics - Application of Derivative Question with Solution | TestHub

MathematicsApplication of DerivativeTangents & NormalsMedium2 minQB

MathematicsMediumsingle choice

A point $P$ describes the circle $x^{2} + y^{2} = 25$ .

Statement - 1: If the ordinate of $P$ decreases at the rate of $1.5 cm/s$ , then the rate of change of abscissa of the point when ordinate equals 4 cm is 2 cm/s.

Statement - 2: $x d x + y d y = 0$

Options:

Answer:

Solution:

$∵ x^{2} + y^{2} = 25$ $\Rightarrow 2 x d x + 2 y d y = 0 or \frac{d y / d t}{d x / d t} = - \frac{x}{y}$ $\Rightarrow \frac{- 1.5}{d x / d t} = - \frac{3}{4} (∵ x = 25 - y^{2} = 3) or \frac{d x}{d t} = \frac{1.5 \times 4}{3} = 2 cm / s$

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

⏱ 2mℹ️ Source: QB

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