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Question

The locus of the centres of the circles which touch the given two circles externally is

A
Pair of lines
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B
Ellipse
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C
Hyperbola
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D
Circle
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Solution

The correct option is B Hyperbola
r1+r=(h+g1)2+(k+f1)2(1)
r2+r=(h+g2)2+(k+f2)2(2)
from (2) & (1)
(r2r1)=(h+g2)2+(k+f2)2(h+g1)2+(k+f1)2
So, difference of distances from two points (g1f1) and
(g2f2) is constant (r2r1) is a locus of
hyperbola.
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