1. Tardigrade
  2. Question
  3. Mathematics
  4. The parametric representation (3+t2, 3 t-2) represents a parabola with

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

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

Conic Sections

Solution:

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