Question

If the coordinates of the vertex and focus of a parabola are (−1, 1) and (2, 3) respectively, then write the equation of its directrix.

Answer 1

Given:
The vertex and the focus of a parabola are (−1, 1) and (2, 3), respectively.

∴ Slope of the axis of the parabola = $\frac{3-1}{2+1}=\frac{2}{3}$

Slope of the directrix = $\frac{-3}{2}$

Let the directrix intersect the axis at K (r, s).

∴ $$\begin{gathered} \frac{r+2}{2}=-1,\frac{s+3}{2}=1 \\ \Rightarrow r=-4,s=-1 \end{gathered}$$

Now, required equation of the directrix:

$\left(y+1\right)=\frac{-3}{2}\left(x+4\right)$
$\Rightarrow 3x+2y+14=0$