SOLUTION: Find the equation of the circles which is tangent to the line 5x+y=1. Identify and sketch three members of the family of circles

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Question 1021364: Find the equation of the circles which is tangent to the line 5x+y=1. Identify and sketch three members of the family of circles

Answer by Alan3354(69443) About Me  (Show Source):
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Find the equation of the circles which is tangent to the line 5x+y=1. Identify and sketch three members of the family of circles
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The centers of the circles is at point (m,n).
Find the distance from (m,n) to the line = radius.
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Distance from a point (m,n) to a line Ax + By + D = 0 is
%28Am+%2B+Bn+%2B+D%29%2Fsqrt%28A%5E2%2BB%5E2%29
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--> r = |5m + n + 1|/sqrt(26)
r%5E2+=+%285m+%2B+n+%2B+1%29%5E2%2F26
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Pick a point (m,n)
%28x-m%29%5E2+%2B+%28y-n%29%5E2+=+%285m+%2B+n+%2B+1%29%5E2%2F26