Q. 54.0( 45 Votes )
Find perpendicular distance from the origin to the line joining the points 
and 
Answer :
The equation of the line joining the points (cosƟ, sinƟ) and (cosɸ, sinɸ) is given by
⇒ y(cosɸ-cosƟ) – sinƟ(cosɸ-cosƟ) = x(sinɸ-sinƟ) – cosƟ(sinɸ-sinƟ)
⇒ x(sinƟ- sinɸ) + y(cosɸ- cosƟ) + cosƟsinɸ - cosƟsinƟ – sinƟcosɸ + sinƟcosƟ = 0
⇒ x(sinƟ- sinɸ) + y(cosɸ- cosƟ) + sin(ɸ-Ɵ) = 0
Ax + By + C = 0, where A = sinƟ- sinɸ, B = cosɸ- cosƟ, and C = sin(ɸ-Ɵ)
It is known that the perpendicular distance (d) of the line Ax + By + C = 0 from a point
(x1, y1) is given by
Thus, the perpendicular distance (d) of the given line from point (x1, y1) =(0,0) is
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