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Find the equation of the circles which touches the line 2x-y=1 at (1,1) and the line 2x+y=4.

Find the equation of the circles which touches the line 2x-y=1 at (1,1) and the line 2x+y=4.

Grade:11

1 Answers

Vikas TU
14149 Points
4 years ago
Dear Student,
family of circles touching given line at given point is given by: (x-1)^2 + (y-1)^2 + k(2x – y – 1 ) =0
 Now centre of circle = ( 1-k , (k+1)/2 )
This must be at a distance of radius from 2x+y = 4
Radius = k√5 /2
D= (2(1-k) + (k+1)/2 -4) / √5
Put D= radius to get k=-3/8
Put the value of k in family of circles to get equation                                
Cheers!!
Regards,
Vikas (B. Tech. 4th year
Thapar University)

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