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

Options

A. A pair of straight lines
B. An ellipse
C. A parabola
D. A hyperbola

Answer

C

Explanation

`(x+y)/(2)=t^(2)+1,(x-y)/(2)=t`
Eliminating, we get `2(x+y)=(x-y)^(2)+4`
Since second terms form a perfect square, it represents a parabola.