Question

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

• A. 3x+2y+14=0
• B. 3x+2y-25=0
• C. 2x-3y+10=0
• D. none of these

Answer 1

The correct option is A

3x+2y+14=0

Given:

The vertex and the focus of a parabola are (-1,1) and (2,3) respectively

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

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

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

$\therefore \frac{r+2}{2}=-1,\frac{s+3}{2}=1$

$\Rightarrow r=-4,s=-1$

Equation of the directrix : $(y+1)=\frac{-3}{2}(x+4)$

$\Rightarrow 3x+2y+14=0$