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

(x_{1}, y_{1}) is given by

Thus, the perpendicular distance (d) of the given line from point (x_{1}, y_{1}) =(0,0) is

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