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

a pair of straight lines

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an ellipse

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a parabola

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a hyperbola

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Solution

The correct option is C a parabola
$\frac{x + y}{2} = t^{2} + 1, \frac{x - y}{2} = t$
Eliminating,
$t, 2 (x + y) = (x - y)^{2} + 4$
Since 2nd degree terms form a perfect square, it represents a parabola.

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Similar questions

x = t^{2} + t + 1, y = t^{2} - t + 1

x = t^{2} + t + 1, y = t^{2} - t + 1

x = t^{2} + 2 t + 2, y = t^{2} + 2 t + 2

x = t^{2} + t + 1, y = t^{2} - t + 1

x = t^{2} + t

y = t^{2} - t

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