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```        PLEASE solve the question of shortest distance between parabolas
by the approach given by you sir and post it completely solved```
7 years ago

Ramesh V
70 Points
```										For this particular problem, if you draw a diagram you'll see that the  two parabolas are symmetric about the line y=x. So the shortest distance  between them will be between the two points where the tangents are  parallel to that line. The points on the parabolas where the tangents have gradient 1 are   on , and  on . The distance between these points is (3*21/2) /4 . In general, if you can't use that sort of symmetry to simplify the  problem, you would have to find the equation of the normal at a general  point on one curve. Then find the point(s), if any, where that line  meets the other curve, determine the distance along the normal to the  closest point on the other curve, and finally minimise that distance.
--
regards
Ramesh
```
7 years ago
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