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). 

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

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

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