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+y2−2x−2λy−8=0 After rearranging it We get, (x2+y2−2x−8)−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+y2−2x−8=0 and y=0 x2+y2−2x−8=0 - - - - - - -(1) y=0 - - - - - - -(2) Solving equations (1) & (2) x2−2x−8=0 or (x−4)(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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