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Question

The common tangent to the circles x2+y2=4 and x2+y2+6x+8y24=0 also passes through the point :

A
(6,4)
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B
(6,2)
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C
(4,2)
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D
(4,6)
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Solution

The correct option is B (6,2)
x2+y2=4
Centre is C1(0,0) and radius, r1=2
x2+y2+6x+8y24=0
Centre is C2(3,4) and radius, r2=7

Distance between centres, C1C2=5=|r1r2|
Therefore, the circles touch internally.
Therefore, equation of common tangent is
S1S2=0
6x+8y=20
or, 3x+4y=10
(6,2) lies on the above common tangent.

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