Question

The equation of the directrix of the parabola whose vertex and focus are (1,4) and (2,6)

• A. x+2y=4
• B. x-y=3
• C. 2x+y=5
• D. x+3y=8

Answer 1

The correct option is A

x+2y=4

Given:

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

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

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

Let the directrix intersect the axis at k(r,s)

$\therefore \frac{\frac{r}{2}}{2}=1,\frac{\frac{s}{6}}{2}=4$

$\Rightarrow r=0,s=2$

Equation of the directrix (y-2)=$\frac{1}{2}(x-0)$

$\Rightarrow x+2y=4$