Question

The curve described parametrically by $x=t^2+2t-1,y=3t+5$ represents

• A. an ellipse
• B. a hyperbola
• C. a parabola
• D. a circle

Answer 1

Answer: (C)

Given $x=t^2+2t-1\&y=3t+5$
$\Rightarrow x=t^2+2t+1-2\&y=3t+3+2$
$\Rightarrow x=(t+1{)}^2-2\&y=3(t+1)+2(2)$
$\Rightarrow (t+1)=\sqrt{x+2}$ .......... (1)
$\therefore$ Equation (2) becomes [using equation (1)]
$y=3\sqrt{x+2}+2$
$\Rightarrow y-2=3\sqrt{x+2}$
squaring both sides, we get
$(y-2{)}^2=9(x+2)$
$\Rightarrow Y^2=9X$ where $Y=y-2\&X=x+2$
This equation represents a parabola