Question

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

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

Answer 1

Answer: (C)

a parabola

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

$x+y=2(t^2+1)$ and $x-y=2t$

$y=t^2-t+1x+y=2(t^2+1)x-y=2[{\left(\frac{x+y}{2}\right)}^2+1]2(x+y)=(x-y)+4x+y=Yx-y=X2Y=X^2+4X^2=2(Y-2)$

Which is a parabola.