Question

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

• A. Circle
• B. Parabola
• C. An ellipse
• D. Hyperbola

Answer 1

The correct option is B Parabola

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

By elimination of $t$

$t=\frac{y+1}{2}$
$x={\left(\frac{y+1}{2}\right)}^2+\frac{y+1}{2}$

$y^2+4y-4x+3=0$
On comparing with $a{x}^2+b{y}^2+2hxy+2gx+2fy+c=0$

we have $a=0,b=1,g=-2,f=2,h=0,c=3$
$\Delta =abc+2fgh-a{f}^2-b{g}^2-c{h}^2=-4\ne 0$
and $h^2-ab=0\Rightarrow h^2=ab$
So, the given equation is a parabola