Circle 4 Question 15

15. 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, then the coordinates of the centre of C2 are… .

(1988,2M)

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Answer:

Correct Answer: 15. 95,125 and 95,125

Solution:

  1. Given, C1:x2+y2=16

and let C2:(xh)2+(yk)2=25

Equation of common chords is S1S2=0

2hx+2ky=(h2+k29)

Its slope =hk=34

[given]

If p be the length of perpendicular on it from the centre (0,0) of C1 of radius 4 , then p=h2+k294h2+4k2.

Also, the length of the chord is

2r2p2=242p2

The chord will be of maximum length, if φ=0 or h2+k29=0h2+169h2=9

h=±95k=125

Hence, centres are 95,125 and 95,125



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