If a chord of a circle x 2 + y 2 – 4x – 2y – c = 0 is trisected at the points (1/3, 1/3) and (8/3, 8/3), then c = ………….
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Ans. 0020
Sol. Equation of the line joining the given points is
y = x and the distance between them is 
i.e. 7 
/3.
If PQ is the chord of the given circle which is trisected at these points then equation of PQ is y = x and the length of this chord is 
= 
. Let C(2, 1) be centre of the given circle and CL be the perpendicular from C to PQ, then the radius of the given circle is 
= (2) 2 + (1) 2 + c
= (7/ 
) 2 + (1/ 
) 2 = 25 ⇒ c = 20.
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