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The length of latus-rectum of the parabola whose parametric equation is $x = t^{2} + t + 1$ and $y = t^{2} - t + 1$ , where $t \in R - \{0\}$ is equal to

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$\sqrt{4}$

$\sqrt{2}$

answer is A.

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Detailed Solution

x = t² + t + 1, y = t² - t + 1
$\Rightarrow \frac{x - y}{2} = t$
Eliminate t $\Rightarrow$ (x - y)² = 2(x + y + 2)
$\Rightarrow {(\frac{x - y}{\sqrt{2}})}^{2} = \sqrt{2} (\frac{x + y + 2}{\sqrt{2}})$
Hence LLR = $\sqrt{2}$

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