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The coordinates of the point P on the curve $x = a (θ + S i n θ)$ , $y = a (1 - C o s θ)$ , where tangent is inclined at an angle $\frac{π}{4}$ to the x-axis are

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$(a (\frac{π}{2} - 1), a)$

$(a \frac{π}{2}, a)$

$(a (\frac{π}{2} + 1), a)$

$(a, a)$

answer is B.

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Detailed Solution

$\frac{d y}{d x} = \frac{a (\sin θ)}{a (1 + \cos θ)} = T a n \frac{θ}{2}$
$\Rightarrow \frac{θ}{2} = \frac{π}{4} \Rightarrow θ = \frac{π}{2}$

$P = (a (\frac{π}{2} + 1), a)$

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