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how to find the shortest distance between 2 curves rather than straight line.

how to find the shortest distance between 2 curves rather than straight line.

Grade:12

6 Answers

Ashwin Muralidharan IIT Madras
290 Points
9 years ago

Hi Sarthak,

Consider A(x1,y1) to be the point on the curve C1 and

B(x2,y2) to be the point on the curve C2.

A will satisfy C1, B will satisfy C2.

From these two you will get relation between x1 and y1

and also between x2 and y2.

Now distance between A and B = distance formula = √[(x1-x2)2+(y1-y2)2].

Now this distance has to be minimised based on the relation between x1,y1 and relation between x2,y2.

This is the standard aproach.

But based on specific questions(where curves are say two circles), you can use different approaches like visualising the two circles, and the two points on the circle should be on the line joining the centres.

Different approaches can be used for different curves.

All the best.

Regards,

Ashwin (IIT Madras).

Aman Bansal
592 Points
9 years ago

Dear Sarthak,

shortest distance b/w two curves is the distance along their common normal.....so find the eqn of common norma at a point of any curve and then solve it wid another curve u will get two points of intersection,,,,now calculate distance using distance formula

Best Of Luck...!!!!

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Aditya srinivas
52 Points
4 years ago
First find out the slope of one of the line or curve. Consider it as closest point and then find out the point on another curve which is parallel to the point we got then the distance between 2 points gives smallest distance
In Class Eleventh
11 Points
3 years ago
I don`t know who is that Aman Bansal, but that AskIITians Expert has got his answer wrong. That relation is not true for general curves. Consider two parabola y²=x and y²=x+1, the common normal is x-axis but the distance is longest along x-axis. Not to mention that he is an EXPERT. XD
tushar
13 Points
3 years ago
by drawing normal and passing it from another curve, thus if two curvs  are  circle and parabola  resp.  then  you can take eq of normal which passes through the circle ,hence equate distance (radius)
Rishi Sharma
askIITians Faculty 646 Points
9 months ago
Dear Student,
Please find below the solution to your problem.

Consider A(x1,y1) to be the point on the curve C1 and B(x2,y2) to be the point on the curve C2.
A will satisfy C1, B will satisfy C2.
From these two you will get relation between x1 and y1 and also between x2 and y2.Now distance between A and B
= distance formula
= √[(x1-x2)2+(y1-y2)2].
Now this distance has to be minimised based on the relation between x1,y1 and relation between x2,y2.

Thanks and Regards

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