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.

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#### Solution

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

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

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