First slide

Parabola

Question

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

Moderate

A

a pair of straight lines
B

an ellipse
C

a parabola
D

a hyperbola

Solution

$\frac{x + y}{2} = t^{2} + 1, \frac{x - y}{2} = t$
Eliminating t , we get
$2 (x + y) = (x - y)^{2} + 4$
Since the second-degree terms form a perfect square, it
represents a parabola $(also, Δ \neq 0)$

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