Question

The parametric representation $\left(3+t^2,3t-2\right)$ represents a parabola with

• A. focus at $(-3,-2)$
• B. vertex at $(3,-2)$
• C. directrix $x=-5$
• D. all of these

Answer 1

Answer: (B)

We have, $x=3+t^2$ and $y=3t-2$
$\Rightarrow x-3=t^2$ and $y+2=3t$
$\Rightarrow (y+2{)}^2=9(x-3)$
which is a parabola with vertex at $(3,-2)$, focus at $\left(\frac{21}{4},-2\right)$ and directrix $x=\frac{3}{4}$.