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Question

If r is the radius of circle which touches both the coordinate axes and passes through (2,1), then which of the following is/are true?

A
least value of r is 1.
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B
greatest value of r is 6.
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C
sum of all possible values of r is 6.
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D
there exist two circle with the given conditions.
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Solution

The correct option is D there exist two circle with the given conditions.
Since, circle is touching both the axes and passing through (2,1), it has to lie in 2nd quadrant.
So, the centre =(r,r), where r is the radius.

Therefore, equation of circle is (x+r)2+(yr)2=r2
Above circle is passing through (2,1), so
(2+r)2+(1r)2=r2r24r+4+r22r+1=r2
r26r+5=0(r1)(r5)=0r=1,5

Least value of r is 1,
Greatest value of r is 5.
That means, there exist two circles.
Sum of all possible values of r is 6.

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