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If the sum of coordinates of point of contact of the circles x2 + y2 - 4x - 2y +4=0 and x2 + y2 - 12x - 8y+ 36 =0 is Q then the value of ( Q - 25) is? ?????

If the sum of coordinates of point of contact of the circles x2 + y2 - 4x - 2y +4=0 and x2 + y2 - 12x - 8y+ 36 =0 is Q then the value of ( Q - 25) is? ?????

Grade:11

1 Answers

Sunil Kumar
askIITians Faculty 183 Points
8 years ago

The centre and radius of : 

C1 : (2,1) , rad = 1unit

C2 : (6,4) , rad = 4 units

Let the point of touching be Q(x,y)

If a line is drawn through the point of contact taking the centres in one line then , the point of contact divides the line in the ratio 1:4.

So apply the section formula to obtain the point Q.

It comes to be (14/5,8/5)

Also , I think it should be Q*25 and not (Q-25), but if it is (Q-25) the answer is (-103/5)

 

Thanks & Regards
Sunil Kumar, 
askIITians Faculty
M.Sc., IIT Kharagpur

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