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# If the vertex and the focus of a parabola are $(-1,1)$ and $(2,3)$ respectively then the equation of the directrise , is

$\begin{array}{1 1}(A)\;3x+2y+14=0 \\(B)\;3x+2y-25=0 \\(C)\;2x-3y+10=0 \\(D)\;none\;of\;these \end{array}$

Can you answer this question?

Equation of the axis of symmetry
$y-1=\large\frac{3-1}{2+1}$
=> $2x-3y+5=0$
Let co-ordinate of the point of interested of direction and axis of symmetric be $(x_1,y_1)$ then
$\large\frac{x_1+2}{2}$$=2^{-1} => x_1=-4 \large\frac{y_1+3}{2}$$=1$
$y_1=-1$
equation of the directrix is
$3(x+4)+2(y+1)=0$
=> $3x+2y+14=0$
Hence A is the correct answer.
answered Apr 10, 2014 by

+1 vote