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Question

If the circle C1:x2+y2=16 intersects another circle C2 of radius 5 in such a manner that the common chord of maximum length 8 has a slope equal to 34, then coordinates of centre of C2 are -
  1. (95,125)
  2. (95,125)
  3. (95,125)
  4. (95,125)

A
(95,125)
B
(95,125)
C
(95,125)
D
(95,125)
Solution
Verified by Toppr

The maximum length of chord = Diameter of circle C1=8 units
Now, equation of the chord of slope 34,
3x4y=0.
The center of circle C2 must be on the line perpendicular to the chord.
So, the center of the circle C2 can be written as (3a,4a)
x1=3a,y1=4a
Where a common factor.

As the chord shown in image, we get AB=5 units using pythagoras theorem.

Hence,
Using sectional formula from a point to a line,
3×(3a)54×(4a)5=85
25a=15
=>a=35.

Now,
The center of the circle C2 can be written as (3×35,4×35)=(95,125).


983195_769264_ans_75b88584b684456b88f422b6792fc3fd.jpg

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