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Question

If the two circles x2+y2+2g1x+2f1y=0&x2+y2+2g2x+2f2y=0 touch each then

A
f1g1=f2g2
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B
f1g1=f2g2
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C
f1f2=g1g2
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D
none
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Solution

The correct option is B f1g1=f2g2

Since the 2 circles touch each other

C1C2=r1±r2

(g1g2)2+(f1f2)2=g21+f21±g22+f22

2g1g22f1f2=±2(g21+f21)(g22+f22)

(g1g2)2+(f1f2)2+2g1g2f1f2=(g1g2)2+(f1f2)2+(g1f2)2+(f1g2)2

2=g1f2g2f1+g2f1g1f2

Let g1f2g2f1=a

2=a+1aa2+2a+1=0

a=1g1f2g2f1=1

f1g1=f2g2


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