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# 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. - Mathematics

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 (rs).

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

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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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 25 Parabola
Exercise 25.2 | Q 9 | Page 28
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