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Show that the locus of point of intersec...

Show that the locus of point of intersection of perpendicular tangents to the parabola `y(2)=4ax` is the directrix x+a=0.

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Assertion (A) : The locus of the point of intersection of perpendicular tangents to y^(2) = 4ax is its directrix. Reason (R) : If theta is acute angle between the pair of tangents drawn from (x_(1),y_(2)) to parabola S =0 then tan theta= (sqrt(S_(11)))/(|x_(1)+a|) The correct answer is