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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 (x−3)2+y2=1. A common tangent of the two circle 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+2√2y=6Common tangent to both the circle is B divides C1:C2 in 2:1 externally ∴ B(6,0) Let the equation of common tangent be ⇒ y−0=m(x−6) ⇒ mx−y−6m=0 Tangent to circle of radius 2 ∴ |6m|√1+m2=2 ⇒ m=±12√2 Equation of tangent x+2√2y=6 or x−2√2y=6

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