If the circles x2+y2=a2 and x2+y2−2gx+g2−b2=0 touch each other externally, then
A
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B
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C
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D
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Solution
The correct option is D For Second circle: x2+y2−2gx+g2−b2=0 Centre =C2(−h,−k)=(g,0) and radius =r2=√h2+k2−c =√(−g)2+02−g2+b2 =√g2−g2+b2 =√b2 ∴r2=b Since, the two circles touch each other externally, So, C1C2=r1+r2 ⇒√(g−0)2+(0−0)2=a+b ⇒√g2=a+b ∴g=a+b