33I think pole and polar is not in syllabus as far as i know??
If ax+by+c=0 is the polar of (1,1) w.r.t the circle x2+y2-2x+2y+1=0 and H.C.F of a,b.c is equal to one then a2+b2+c2= ?
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3311Now the question is what is the polar?!
I dont think u should worry about it.. It is definitely out of syllabus :)
But if u still want, i will tel u what it is !
Syllabus!
Two dimensions: Cartesian coordinates, distance between two points, section formulae, shift of origin.
Equation of a straight line in various forms, angle between two lines, distance of a point from a line; Lines through the point of intersection of two given lines, equation of the bisector of the angle between two lines, concurrency of lines; Centroid, orthocentre, incentre and circumcentre of a triangle.
Equation of a circle in various forms, equations of tangent, normal and chord.
Parametric equations of a circle, intersection of a circle with a straight line or a circle, equation of a circle through the points of intersection of two circles and those of a circle and a straight line.
Equations of a parabola, ellipse and hyperbola in standard form, their foci, directrices and eccentricity, parametric equations, equations of tangent and normal.
62hmm.. well pole and polar are not in syllabus as shailesh and priyam pointed out..
the problem is not very tough as such. Pole and polar are simple concepts.. even simpler for a circle!
33ok let me see the basic def of it then i'll try it...
it never pays 2 know a thing....
62http://en.wikipedia.org/wiki/Pole_and_polar
read this! it is good enuf to know!
1polar eqn: T=0
=> 2x1+2y1 - (x+x1) + (y+y1) +1 =0
here (x1,y1) = (1,1).
putting it... 2 + 2 -1 -x +1+y +1 =0 => -x+y+5=0
then compare this with the eqn of polar given: ax +by +c=0...
a=-1, b=1,c=5 (we will not take muliples of these coz its given that HCF is 1)
so, A^2+B^2+C^2=1+1+25=27... (hope this is the ans... correct me if wrong...)
62But not in IIT JEE even though it is not a very difficult question :)
But good that u got ur solution! :)
62x2+y2-2x+2y+1=0
The polar will be
xx1+yy1-(x+x1)+(y+y1)+1 where (x1=1 and y1=1)
so this will be
2y+1
compare with ax+by+c=0
a=0, b=2, c=1
so the given expression is 5 :)
1oh shit!
wat a shameful mistake .... :(
i wrote the T=0 eqn. wrong.. :( chhi!
and also never noticed it.... chhi!