If The Two Circles x2 + y2 + 2gx + 2fy = 0 And x2 + y2 + 2g1x + 2f1y = 0 Touch Each Other, Then

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Question

If the two circles x2 + y2 + 2gx + 2fy = 0 and x2 + y2 + 2g1x + 2f1y = 0 touch each other, then

Solution

Correct option is

f1g = f g1

Both the circles pass through the origin. If they touch each other then the tangents to the two circle at the origin is same. 2gx + 2fy = 0 and 2g1x + 2f1y= 0 represent the same line.  

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