Question

line from the origin.
If p and p' are the perpendicular distance from the origin upon the straight lines whose
= a and x cos 0 - y sin 0 -
equations are x sec 0 + y cosec o
a cos' o. prove that
4p? + (2p') = 4a? cos.​

Answer 1

Answer:

a²

Step-by-step explanation:

Given : Equations of lines 

xsecθ+ycscθ=a⇒xsecθ+ycscθ−a=0   ...(1)

and xcosθ−ysinθ=acos2θ⇒xcosθ−ysinθ−acos2θ=0    ...(2)

We know that the coordinates of the origin (x1,y1)=(0,0).

We also know that the standard equation of the line is ax+by+c=0.

Comparing Eqs. (1) and (2) with the standard equation, we get

a1=secθ,b1=cscθ,c1=−a,a2=cosθ,b2=−sinθ and c2=−acos2θ

Therefore,the length of the perpendicular from the origin to the line (1) is given by

(p)=a2+b2∣ax1+by1+c1∣=sec2θ+csc2θ∣secθ×(0)+cscθ×(0)−a∣

= a²

Answer 2

Answer:

calculate the electric field between two metal plates 3mm apart connected to a 3V battery