Q. 65.0( 1 Vote )
Find the equation of the straight line upon which the length of the perpendicular from the origin is 2, and the slope of this perpendicular is 
.
Answer :
Assuming:
The perpendicular drawn from the origin make acute angle α with the positive x–axis. Then, we have, tanα = 5/12
We know that, tan(180∘ + α) = tanα
So, there are two possible lines, AB and CD, on which the perpendicular drawn from the origin has a slope equal to 5/12 .
Given:
Now tan α = 5/12
⇒ 
Explanation:
So, the equations of the lines in normal form are
Formula Used: x cos α + y sin α = p
⇒ x cos α + y sin α = p and x cos(180° + α) + ysin(180° + α) = p
⇒ x cos α + y sin α = 2 and –x cos α – ysin α = 2
cos (180° + θ) = – cos θ , sin (180° + θ) = – sin θ
⇒ 
and 12x + 5y = – 26
Hence, the equation of line in normal form is 
and 12x + 5y = – 26
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