Equation of the curve whose polar sub tangent r2d-dr is constant

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Standard XII

Mathematics

Variable Separable Method

Equation of t...

Question

Equation of the curve whose polar sub tangent $r^{2} \frac{d θ}{d r}$ is constant

r (θ + c) + k = 0

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r^{2} (θ + c) = 2 k

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r (θ - c) = k^{2}

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r θ = c

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Solution

The correct option is B $r (θ + c) + k = 0$
Let the constant length of the polar subtangent be $a$
Therefore as given in the question $r^{2} \frac{d θ}{d r} = a$
which is the differential equation of the required curve
To solve, put it into the form
$d θ = a (\frac{1}{r^{2}}) d r \Rightarrow \int d θ = \int a (\frac{1}{r^{2}}) d r$
$\Rightarrow θ + c = - \frac{a}{r} \Rightarrow r (θ + c) + a = 0$

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Equation of the curve whose polar sub tangent r2dθdr is constant

The correct option is B r(θ+c)+k=0Let the constant length of the polar subtangent be aTherefore as given in the question r2dθdr=awhich is the differential equation of the required curveTo solve, put it into the form dθ=a(1r2)dr⇒∫dθ=∫a(1r2)dr⇒θ+c=−ar⇒r(θ+c)+a=0

Equation of the curve whose polar sub tangent $r^{2} \frac{d θ}{d r}$ is constant