Q.

The distance between the chords of contact of tangents to the circle x2+y2+2gx+2fy+c=0  from the origin and the point  (g,f) is:

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a

g2+f2c2

b

g2+f2c2g2+f2

c

g2+f2

d

g2+f2+c2g2+f2

answer is D.

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Detailed Solution

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Equation of chord of contact of p(x1,y1) with respect to the circle s=0  is  s1=0
Chord of contact of (0,0) is gx+fy+c=0  Chord of contact of (g,f) is gx+fy+g2+f2+c2=0  Distance between them=g2+f2+c2-cg2+f2=g2+f2c2g2+f2

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The distance between the chords of contact of tangents to the circle x2+y2+2gx+2fy+c=0  from the origin and the point  (g,f) is: