SOLUTION: There are two circles which passes through the point (1,2) and also touch both axes.Find the equation of the two possible circles.?! Please recomend any coordinate geometory textbo

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Question 990645: There are two circles which passes through the point (1,2) and also touch both axes.Find the equation of the two possible circles.?! Please recomend any coordinate geometory textbook for me
Answer by anand429(138) About Me  (Show Source):
You can put this solution on YOUR website!
Since the circle touches both the axes,
we, can take center of circle as (r,r) where r is also radius of circle.
(Draw a fig. to see clearly)
So, equation of circle can be given by,
%28x-r%29%5E2+%2B+%28y-r%29%5E2+=+r%5E2 --------------(i)
Since, it passes through (1,2),
%281-r%29%5E2+%2B+%282-r%29%5E2+=+r%5E2
=> +r%5E2-2r%2B1+%2B+r%5E2-4r%2B4+=+r%5E2
=> r%5E2-6r%2B5+=+0
=> %28r-1%29%28r-5%29+=+0
So r = 1 or r =5
So, clearly we have two circles with centres at (1,1) and (5,5) with radii 1 and 5 respectively.
Equation of circles be given by putting value of r in eqn (i):-
%28x-1%29%5E2+%2B+%28y-1%29%5E2+=+1%5E2
and
%28x-5%29%5E2+%2B+%28y-5%29%5E2+=+5%5E2
(Simplify it.)
A good coordinate geometry book:- "The Elements of Coordinate geometry" by S. L. Loney