Let a line be drawn through the fixed pt. P(a , b) to cut the circle x 2 + y 2 = r 2 at A and B. If PT is the length of tangent drawn from P, then -
Text Solution
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(a, b, c)
Equation of line through (a, b) is
= 
= λ say …(1)
λ is the distance of (x, y) from P (a, b)
( λ cos θ + a, λ sin θ + b) lies on the circle x 2 + y 2 = r 2 λ
2 + 2 λ (a cos θ + b sin θ ) + a 2 + b 2 – r 2 =0 …(2)
line (1) meets the circle in A and B then PA and PB are the roots of equation (2) So PA.PB = a 2 + b 2 – r 2 = T 2 T
2 = S 1 = a 2 + b 2 – r 2 PA, PT, PB are in G.P.
PA.PB = constant
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