Find the equation

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