Find the equation of the circle which is tangent to the line at and passes through the point

I've got the best way to solve this problem , do you know how i solved it ?

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- June 21st 2009, 04:53 AMsimplependulumFind the best way to solve this question
Find the equation of the circle which is tangent to the line at and passes through the point

I've got the best way to solve this problem , do you know how i solved it ? - June 21st 2009, 05:32 AMTheAbstractionist
Well, I did the usual textbook stuff

__Spoiler__:

Nevertheless the method did not appear to be particularly quick, so I guess you have a quicker solution. - June 22nd 2009, 12:28 AMsimplependulum
Let F be a family of circles such that all members of the family F touch the line at .

Then F should be .

Since the required member passes through ,

it satisifies .

Therefore ,

Finally substitute back to F ,

The required equation is :