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 

Options

•  3x + 2y + 14 = 0 

• 3x + 2y − 25 = 0 

• 2x − 3y + 10 = 0 

•  none of these. 

Answer 1

 3x + 2y + 14 = 0 

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). 

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

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

\[\Rightarrow 3x + 2y + 14 = 0\]