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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