Question

The parametric point $(3+t^2,3t-2)$ represents a parabola with

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

Answer 1

The correct option is B vertex at $(3,-2)$

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