Question

# If ax+by+c=0 is the polar of (1,1) for the circle x2+y2−2x+2y+1=0 and H.C.F. of b,c is equal to 1, then the value of a2+b2+c2 is 35015

Solution

## The correct option is B 5Given circle is x2+y2−2x+2y+1=0 Now, the equation of polar is T=0⇒x(1)+y(1)−(x+1)+(y+1)+1=0⇒2y+1=0⇒0⋅x+2⋅y+1=0 Given equation of polar is ax+by+c=0, so  a=0 Now,  b2=c1=k⇒b=2k,c=k As the H.C.F. of b,c is 1, so b=2,c=1∴a2+b2+c2=5

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