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Question

A tangent PT is drawn to the circle x2+y2=4 at the point P(3,1). A straight line L, perpendicular to PT is a tangent to the circle (x3)2+y2=1
A common tangent of the two circles is

A
x=4
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B
y=2
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C
x+3y=4
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D
x+22y=6
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Solution

The correct option is D x+22y=6
Here, equation of common tangent be

y=mx±21+m2
Which is also the tangent to
(x3)2+y2=1
|3m0+21+m2|m2+1=1 3m+21+m2=±1+m2 3m=31+m2or 3m=1+m2 m2=1+m2 or 9m2=1+m2mϵϕ or m=±122 y=±122x±21+18 y=±x22±622 22y=±(x+6) x+22y=6

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