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If two circles (x+4)2+y2=1 and (x−4)2+y2=9 are  touched externally by a variable circle, then locus of centre of variable circle is

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a

x215−y21=1

b

x24−y212=1

c

x212−y24=1

d

x21−y215=1

answer is D.

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Detailed Solution

CS=r+1CS′=r+3CS−CS′=2Locus of C is hyperbola with (-4,0) and (4, 0) as foci. Here 2a=2, so a=1 and 2ae=8, so ae=4b2=a2e2−1=15
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