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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.
Solution
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: \[\left( y + 1 \right) = \frac{- 3}{2}\left( x + 4 \right)\]
\[\Rightarrow 3x + 2y + 14 = 0\]
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