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x+y=2 and x-y=2 are tangents on a parabola at (1,1) and (4,2) respectivley. Which of the followings is/are correct. |
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Answer» EQUATION of directrix is `x+3y=2` Point of intesection `=(2,0)` mid-point of `(1,1)` & `(4,2)` is `(5/2,3/2)` Slope of axis`=(3/2-0)/(5/2-2)=3` Equation of directrix `y=-1/3(x-2)` Equation of directrix `y=-1/3(x-2)` `x+3y=2` `AB` is focal CHORD, `BS=` (`_|__(R)` distance from `B` on directrix) `=(4+6-2)/(sqrt(10))=8/(sqrt(10))` `AS=` ( `_|__(r)` distance from `A` on directrix) `=(1+3-2)/(sqrt(10))=2/(sqrt(10))` So, focus divides `AB` in `1:4` RATIOS. So `S=(8/5, 6/5)`
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