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 α given by tan α = $$\dfrac{5}{12}$$ with the positive direction of x–axis.

Asked by Aaryan | 1 year ago |  38

##### Solution :-

Given:

p = 3, α = tan-1 ($$\dfrac{5}{12}$$)

So, tan α = $$\dfrac{5}{12}$$

sin α = $$\dfrac{5}{13}$$

cos α = $$\dfrac{12}{13}$$

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

$$\dfrac{12x}{13}+ \dfrac{5y}{13}=3$$

12x + 5y = 39

The equation of line in normal form is 12x + 5y = 39.

Answered by Aaryan | 1 year ago

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