A tangent PT is drawn to the circle x 2 + y 2 = 4 at the point P( 
, 1). A straight line L, perpendicular to PT is a tangent to the circle (x – 3) 2 + y 2 = 1.
(i) A common tangent of the two circles is
Text Solution
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Sol. (i) & (ii)
Equation of tangent at 
= 4
(i) 
B divides C 1 C 2 in 2 : 1 externally
∴ B(6, 0)
Hence let equation of common tangent is
y – 0 = m(x – 6)
mx – y – 6m = 0
length of ⊥ r dropped from center (0, 0) = radius
= 2 ⇒ m = ± 
∴ equation is x + 
y = 6 or x – 
y = 6
(ii) Equation of L is
x – 
+ c = 0
length of perpendicular dropped from centre = radius of circle
∴ 
= 1 ⇒ C = –1, –5
∴ x – 
y = 1 or x – 
y = 5
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