Length of latus rectum of the parabola whose parametric equations are $X = t^{2} + t + 1, y = t^{2} - t + 1$ where $t ϵ R$ , is equal to

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Solution

The correct option is C
$x + y = 2 (t^{2} + 1)$ $x - y = 2 t$
$∴ (x + y - 2) = 2 {(\frac{x - y}{\sqrt{2}})}^{2} = \sqrt{2} = (\frac{x + y - 2}{\sqrt{2}})$

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x = t^{2} + t + 1

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