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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

PLEASE solve the question of shortest distance between parabolas


 by the approach given by you sir and post it completely solved

Grade:12

1 Answers

Ramesh V
70 Points
11 years ago

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.

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regards

Ramesh

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