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A normal is drawn to the curve $y = x^{2}$ on it. The length of the portion of the normal intercepted between the axes is

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$\frac{13}{2}$

$\frac{\sqrt{39}}{2}$

$\frac{\sqrt{13}}{4}$

$\frac{\sqrt{45}}{2}$

answer is D.

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Detailed Solution

$y = x^{2} \Rightarrow \frac{dy}{dx} = 2 x \Rightarrow {(\frac{dy}{dx})}_{(111)} = 2$

$∴$ eq of normal is $y - 1 = \frac{- 1}{2} (x - 1)$

$\Rightarrow 2 y - 2 = - x + 1 \Rightarrow x + 2 y = 3$

Length $= \sqrt{9 + \frac{9}{4}} = \frac{\sqrt{45}}{2}$

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