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$The curve described parametrically by x = t^{2} + t + 1, and y = t^{2} - t + 1 represents$

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a pair of straight lines

an ellipse

a parabola

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Correct option is C

x+y2=t2+1,x−y2=tEliminating t , we get2(x+y)=(x−y)2+4Since the second-degree terms form a perfect square, itrepresents a parabola ( also ,Δ≠0)

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The curve described parametrically by x=t2+t+1, and y=t2−t+1 represents

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$The curve described parametrically by x = t^{2} + t + 1, and y = t^{2} - t + 1 represents$