Asked by Anonymous
find orthogonal trajectory of family of circles x^2+y^2+2fy+1=0.
Answers
Answered by
Steve
You have
x^2 + (y+f)^2 = f^2-1
These are circles with center at (0,-f). Clearly the radii of these circles are orthogonal to the curves, and that is the family of lines that pass through (0,-f):
y+f = mx
x^2 + (y+f)^2 = f^2-1
These are circles with center at (0,-f). Clearly the radii of these circles are orthogonal to the curves, and that is the family of lines that pass through (0,-f):
y+f = mx
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