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Show that,the equation of the straight line xcos theta+ysin theta=p can be expressed in the following term: X-pcos theta/-sin theta=y-psin theta/cos theta=r.

Show that,the equation of the straight line xcos   theta+ysin theta=p can be expressed in the following term:
               X-pcos theta/-sin theta=y-psin theta/cos theta=r.
 

Grade:11

1 Answers

Aditya Gupta
2081 Points
5 years ago
let costheta=c and sintheta=s
now write p= ps^2+pc^2
so the eqn xcostheta+ysin theta=p becomes
xc+ys=ps^2+pc^2
c(x – pc)= s(ps – y)
or (x – pc)/s= (ps – y)/c
or (x – pc)/-s= (y – ps)/c= r (say)
 
 

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