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explian the radical axis,pole and polar with their properties.

explian the radical axis,pole and polar with their properties.

Grade:12th Pass

1 Answers

Ashwin Muralidharan IIT Madras
290 Points
12 years ago

Hi Menka,

 

Firstly Radical Axis, Pole and Polar are not there in IIT JEE syllabus. And IITs stick to syllabus, and questions are asked within the gambit of prescribed syllabus.

 

In any case just to give you a brief:

 

Radical Axis is defined in cases of different positions of two circles (It is the locus of all points from where tangents of equal lengths can be drawn to two circles.

A. In case two circles intersect, the line of the common chord outside both the circles is the radical Axis.

B. In case two circles touch each other, Common tangent is the Radical Axis

C. In case two circles have no common point of intersection or do not touch, the radical Axis will be a line perpendicluar to the line joining the centres of the two circles.

 

Pole And Polar:

Polar is the locus of all points, from where all the chords of Contacts drawn to the circle will intersect at a given point "P" called the Pole.

And it can be shown, that Locus of the polar, will be a straight line.

Here is a diagram of that:

These are the basic Concepts.

 

In case you need to know how to get the equations of the Polar, and the Radical Axis, I can send you scanned copies of my IIT JEE notes.

In case you need them, mail me at [ashwin.rsmd@gmail.com]

We are here to solve you querries.

 

Hope that helps.

 

All the best,

Regards,

Ashwin (IIT Madras).

 

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