Question

The product of y the perpendiculars from the two points `(pm 4, 0)` to the line `3x cos phi +5y sin phi =15` is
A. 25
B. 16
C. 9
D. 8

Answer 1

Correct Answer - C
If the length of perpendicular be `p_(1)` from the point (4, 0)
`p_(1)=|(12 cos phi -15)/sqrt((3 cos phi)^(2)+(5 cos phi)^(2))|`
`=(15-12 cos phi)/sqrt((3 cos phi)^(2)+(5 cos phi)^(2))`
If length of perpendicular be `p_(2)` from the point (-4, 0)
`P_(2)=|(-12 cos phi -15)/sqrt((3 cos phi)^(2)+(5 cos phi)^(2))|`
`=((12 cos phi +15))/sqrt((3 cos phi)^(2)+(5 sin phi)^(2))`
`p_(1).p_(2)=((15-12 cos phi)(12 cos phi +15))/((3 cos phi)^(2)+(5 sin phi)^(2))`
`=((225-144 cos^(2) phi))/(9 cos^(2) phi + 25 sin^(2) phi)=(9(25-16 cos^(2) phi))/(25-16 cos^(2) phi)`
`=9`