Find the length of the perpendicular from the origin to the straight line joining the two points whose coordinates are (a cos α , a sin α ) and (a cos β , a sin β ).

Question

Philoid · Accepted Answer

Given:

Coordinates are (a cos α, a sin α) and (a cos β, a sin β).

To find:

The length of the perpendicular from the origin to the straight line joining the two points whose coordinates are (a cos α, a sin α) and (a cos β, a sin β).

Concept Used:

Distance of a point from a line.

Explanation:

Equation of the line passing through (acosα, asinα) and (acosβ, asinβ) is

The distance of the line from the origin is

Hence, the required distance is

Find the length of the perpendicular from the origin to the straight line joining the two points whose coordinates are (a cos α, a sin α) and (a cos β, a sin β).