Question

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

• A. Focus at $(-3,-2)$
• B. Vertex at $(3,-2)$
• C. Directrix $x=-5$
• D. None of these

Answer 1

Answer: (B)

Vertex at $(3,-2)$

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 $(\frac{21}{4},-2)$ and directrix $x=\frac{3}{4}$.