A variable st. line cuts off from the given st. lines concurrent at origin,intercepts ,the sum of reciprocals of which is a non zero constant K.Show that varibale line passes through a fixed pt. whose coordinates are (i=1)Σ(n) cos@i/K , (i=1)Σ(n) sin@i/K where @i is the given n values
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2 Answers
62let the lines be
y=x tan(@i)
let the variable line be y=mx+c
This line cuts y=x tan(@i) at x(tan(@i)-m)=c
x=c/(tan(@i)-m)
y=c.tan(@i)/(tan(@i)-m)
Length fo the inercept is c sec(@i)/(tan(@i)-m)
=c / {(sin(@i) - m cos(@i) }
reciprocal of lenthg of the intercept is {(sin(@i) - m cos(@i) }/c
Sum of the length is constant!!!!
{Σ(sin(@i) - mΣ cos(@i) }/c =K
Does this give the hint???????/
