Question

The equation of the directrix of the parabola whose vertex and focus are (1, 4) and (2, 6) respectively is
(a) x + 2y = 4
(b) x − y = 3
(c) 2x + y = 5
(d) x + 3y = 8

Answer 1

(a) x + 2y = 4

Given:
The vertex and the focus of a parabola are (1, 4) and (2, 6), respectively.

∴ Slope of the axis of the parabola = $\frac{6-4}{2-1}=2$

Slope of the directrix = $\frac{-1}{2}$

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

∴ $$\begin{gathered} \frac{r+2}{2}=1,\frac{s+6}{2}=4 \\ \Rightarrow r=0,s=2 \end{gathered}$$

Equation of the directrix:

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