InterviewSolution
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InterviewSolution
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The number of integer values of k for which the equation `x^2 +y^2+(k-1)x-ky+5=0` represents a circle whose radius cannot exceed 3 is |
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Answer» `x^2+y^2+2gx+2fy+c=0` where centre`=(-g,-f)` `r=sqrt(f^2+g^2-c)` `2g=k-1` `g=(k-1)/2` `2f=-k` `f=-k/2` `c=5` `r<=3` `sqrt(f^2+g^2-c) <=3` `f^2+g^2-c<=9` `k^2/4+(k-1)^2/4-5<=9` `(k^2+(k-1)^2-4xx14)/4<=0` `k^2+(k-1)^2-56<=0` `k^2+k^2-2k+1-56<=0` `2k^2-2k-55<=0` `k=2+-sqrt(4+440)/2xx2` `k=2+-sqrt2(111)/4` `k=1+-sqrt2(111)/2` `(k- (1-sqrt(111)/2)(k-(1+sqrt111/2)` `sqrt111=10.53` `(1-sqrt111)/2=-4.7` `(1+sqrt111)/2=5.7` option `1` |
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