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Question

Consider the family of circles x2 + y2 2x 2λy 8 = 0 passing through two fixed points A and B. Then the distance between the points A and B, is –––––––––––––


A

6

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B

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C

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D

36

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Solution

The correct option is A

6


Given equation of family of circles

x2+y22x2λy8=0

After rearranging it

We get,

(x2+y22x8)2λy=0

Which is of the form of S+λL=0 of families of circles

All the circles passes through the point of intersection of circle x2+y22x8=0 and y=0

x2+y22x8=0 - - - - - - -(1)

y=0 - - - - - - -(2)

Solving equations (1) & (2)

x22x8=0

or (x4)(x+2)=0

x=4,x=2

Point A(4,0)

Point B(2,0)

AB=(4+2)2+=36=6

Distance between point A and B is 6.


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