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Find the equations of the circles whose centers lie on the line 4x + 3y = 2 and which touch the lines x + y + 4 = 0 and 7x - y + 4 = 0 There are 2 solutions to this question...

Find the equations of the circles whose centers lie on the line 4x + 3y = 2 and which touch the lines x + y + 4 = 0 and 7x - y + 4 = 0
 
There are 2 solutions to this question...
 
 

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1 Answers

viswanath
40 Points
9 years ago
Here the two lines are tangents to the circle.
Let the centre of the circle be (a,b). Now, |a+b+4|=r√2 .Also |7a-b+4|=5r√2 and 4a+3y=2         r=radius
Solve these equations and find (a,b)
 The values are (2,-2) and (-4,6).Now find corresponding  r for each values and find the two equations.
 

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