Q. 54.0( 59 Votes )

Find perpen

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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