The length of the perpendicular from the origin to the line `(x sin alpha )/(b)-(y cos alpha )/(a)-1=0` is

Options

A. `(|ab|)/(sqrt(a^(2)cos ^(2)alpha-b^(2)sin ^(2)alpha ))`
B. `(|ab|)/(sqrt(a^(2)cos ^(2)alpha+b^(2)sin ^(2)alpha ))`
C. `(|ab|)/(sqrt(a^(2)sin ^(2)alpha -b^(2)cos ^(2)alpha ))`
D. `(|ab|^(2))/(sqrt(a^(2)sin ^(2)alpha +b^(2)cos ^(2)alpha ))`

Answer

D

Explanation

The length of perpendicular from the origin to the line
` ( x sin alpha )/( b ) - ( y cos alpha ) /( a ) - 1 = 0 ` is
` d = ( | 0 - 0 - 1 | ) /( sqrt (( sin ^ 2 alpha ) /( b ^ 2 ) + ( cos ^ 2 alpha )/( a ^ 2 )) `
` = ( |ab| ^ 2 ) /( sqrt ( a ^ 2 sin ^ 2 alpha + b ^ 2 cos alpha ) `