If The Circle C1, x2 + y2 = 16 Intersects Another Circle C2 of Radius 5 In Such A Manner That The Common Chord Is Of Maximum Length And Has A Slope Equal To (3/4), Find The Co-ordinates Of Centre C2.

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If the circle C1x2 + y2 = 16 intersects another circle C2 of radius 5 in such a manner that the common chord is of maximum length and has a slope equal to (3/4), find the co-ordinates of centre C2.


Correct option is


Let the centre of the circle C2 is Q(hk), Equation of the circle C2 is


or          x2 + y2 – 2xh – 2yk + h2 + k2 – 25 = 0  


And equation of circle   

∴ Equation of common chord is

                       C1 – C2 = 0  


or        2hx + 2ky – (h2 + k2 – 9) = 0                   …(1)

           Slope of this line = –h/k

But, it is given that its slope = 3/4


or                       3k + 4h = 0                        …(2)

Let P be the length perpendicular from P(0, 0) on chord (1), then


Length of this chord AB = 2AM  


This chord has maximum length, then p = 0 then from (3), 

                             h2 + k2 – 9 = 0                        …(4)

Solving (2) and (4) we get 





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