Q. 34.8( 5 Votes )

Find the equation of the line whose perpendicular distance from the origin is 4 units and the angle which the normal makes with the positive direction of x–axis is 15°.

Answer :

Given: p = 4, α = 15°

Concept Used:


Equation of line in normal form.


Explanation:


We know that, cos 15° = cos (45° – 30°) = cos45°cos30° + sin45°sin30°


cos(A – B) = cosAcosB + sinAsinB



And sin 15 = sin (45° – 30°) = sin 45° cos 30° – cos 45° sin 30°


sin (A – B) = sinAcosB – cosAsinB



So, the equation of the line in normal form is


Formula Used: x cos α + y sin α = p



(√3 + 1)x + (√3 – 1)y = 8√2


Hence, the equation of line in normal form is (√3 + 1)x + (√3–1)y = 8√2


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