Let a circle be 2x(x – a) + y (2y – b) = 0, a ≠ 0, b ≠ 0. Then the condition on a and b if two chords each bisected by the x-axis, can be drawn to the circle from 
, is-
Text Solution
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The equation of the circle is
2x(x – a) + y(2y – b) = 0
⇒ x 2 + y 2 – ax – 
y = 0
Let PQ and PR be two chords drawn from P 
such that they are bisected by x-axis.
Let A(t, 0) be the mid-point of PQ. Then, its equation is
tx + 0y – 
(x + t) – 
(y + 0) = t 2 – at
[Using T = S’]
⇒ 
x – 
y = t 2 – 
t
This passes through P 
. Therefore,
= t 2 – 
t
⇒ t 2 – 
at + 
= 0
This should give two distinct values of t for points A and B.
∴ 
a 2 – 4 
> 0
⇒ 
⇒ a 2 > 2b 2
Hence is the correct answer.
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