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 .

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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