Q3 of 169 Page 689

Find the equation of the line which is at a distance of 3 units from the origin such that tan ∝ = where ∝ is the acute angle which this perpendicular makes with the positive direction of the x-axis.

To Find:The equation of the line.


Given : tan ∝ = and p =3 units.


Since tan ∝ = =



Using Pythagoras theorem :


hyp = = = 13 units.


From the figure: cos ∝ = = and sin ∝ = =


Formula used:


equation of the line: x cos ∝+y sin ∝ =p


x () +y × ( ) = 5


Hence ,12x + 5y = 65 is the required equation of the line.


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