find orthogonal trajectory of family of circles x^2+y^2+2fy+1=0.

Answer 1

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

Answer 2

X^2+y^2-cx-100

Answer 3

x2+2y2=c2

Answer 4

x2+y2-c1y=c

Answer 5

Answer for this problem

Answer 6

Orthogonal trajectory of x^2+y^2+2fy+1=0 please give me answer

Answer 7

Give me answer