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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