The length of perpendicular from the point ( ` a cos prop, a sin prop`) upon the striaght line y = x ` tan prop +c ` (where c gt 0) is

Options

A. c
B. `c sin^(2) prop`
C. `c cos prop`
D. `c sec^(2) prop`

Answer

C

Explanation

The length of perpendicular from point (a `cos prop, a sin prop)`
to the line ` x tan prop - y+c = 0 or `
` x sin prop - y cos prop + cos prop =0`
` is | (a cos prop sin prop - a sin prop cos prop + c cos prop)/(sqrt(sin^(2) prop + cos^(2) prop))| = c cos prop`