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  • If the tangents at two points (1,2) and (3,6) on a parabola intersect at the point (1,6), then equation of directrix is  Option: 1 <img a

If the tangents at two points (1,2) and (3,6) on a parabola intersect at the point (1,6), then equation of directrix is
 

Option: 1

\mathrm{2 x+y-8=0 }


Option: 2

\mathrm{ x-2 y+11=0 }


Option: 3

\mathrm{ x+2 y-13=0 }


Option: 4

\mathrm{ 2 x-y+4=0 }


Answers (1)

best_answer

Mid-point of (1,2) and (3,6) is (2,4), line passing through (1,6) and (2,4) is parallel to axis of the parabola (property).

So, slope of its axis is -2 or slope of its directrix is \frac{1}{2}, also in this case tangents are perpendicular. So, (1,6) must lie on directrik,

\mathrm{\therefore \quad y-6=\frac{1}{2}(x-1) \Rightarrow x-2 y+11=0 }

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