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Question

If r is the radius of circle which touches both the coordinate axes and passes through (âˆ’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 options are A least value of r is 1. C sum of all possible values of r is 6. 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+(y−r)2=r2 Above circle is passing through (−2,1), so (−2+r)2+(1−r)2=r2⇒r2−4r+4+r2−2r+1=r2 ⇒r2−6r+5=0⇒(r−1)(r−5)=0⇒r=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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