Question

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

• A. a pair of straight lines
• B. an ellipse
• C. a parabola
• D. a hyperbola

Answer 1

Answer: (C)

$\frac{x+y}{2}=t^2+1,\frac{x-y}{2}=t$
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, $\Delta \ne 0$ ).