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Question

If ax+by+c=0 is the polar of (1,1) for the circle x2+y22x+2y+1=0 and H.C.F. of b,c is equal to 1, then the value of a2+b2+c2 is 
  1. 3
  2. 5
  3. 0
  4. 15


Solution

The correct option is B 5
Given circle is x2+y22x+2y+1=0
Now, the equation of polar is
T=0x(1)+y(1)(x+1)+(y+1)+1=02y+1=00x+2y+1=0
Given equation of polar is ax+by+c=0, so 
a=0
Now, 
b2=c1=kb=2k,c=k
As the H.C.F. of b,c is 1, so
b=2,c=1a2+b2+c2=5

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