Question

Consider the following statements :
1. For an equation of a line,
`x cos q + y sin q = p`, in normal form, the length of the perpendicular from the point (a, b) to the line is
`|a cos q+b sin q+p|`.
2. The length of the perpendicular from the point (a, b) to the line `x/a+y/b=1` is `|(a alpha+b beta-ab)/sqrt(a^(2)+b^(2))|`.
Which of the above statements is/are correct ?
A. 1 only
B. 2 only
C. Both 1 and 2
D. Neither 1 nor 2

Answer 1

Correct Answer - D
The length of perpendicular from `(alpha, beta)` to line
`x cos theta+ y sin theta-p=0`
`|alpha cos theta+ beta sin theta -p|`
`:.` Statement 1 is false.
The length of perpendicular from `(alpha, beta)` to line `x/a+y/b=1`
`x/a+y/b=1 implies bx+ay-ab=0`
So, perpendicular is `|(b alpha+alpha beta-ab)/sqrt(a^(2)+b^(2))|`
`:.` Statement 2 is also false.