Let a circle be given by

                   2x (x – a) + y(2y – b) = 0            (a ≠ 0, b ≠ 0)

Find the condition on a and b if two chords, each bisected by the x-axis, can be drawn to the circle from (ab/2).


Correct option is


The given circle is      2x (x – a) + y(2y – b) = 0  

or                                x2 + y2 – ax – by/2 = 0  

let AB be the chord which is bisected by x-axis at a point M. Let its co-ordinates be (h, 0) 

and let                   



since its passes through (ab/2) we have   


Now there are two chords bisected by the x-axis, so there must be two distinct real roots of h





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