Question

. Find the equation of the straight line at a distance of 3 units from the origin such that the perpendicular from the origin to the line makes an angle a, given by the equation tan =5/12, with the positive direction of the axis of x?​

Answer 1

p = 3, α = tan-1 (5/12) So, tan α = 5/12 sin α = 5/13 cos α = 12/13 The equation of the line in normal form is given by By using the formula, x cos α + y sin α = p Now, substitute the values, we get 12x/13 + 5y/13 = 3 12x + 5y = 39 ∴

Answer 2

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Explanation:

From given condition

equation of line is given as,

x*cos(α)+y*sin(α)=p

& as tanα= 5/12 so from Pythagoras theorem

sinα= 5/13

​cosα= 12/13

⇒12x+5y=39

⇒12x+5y−39=0