Find the equation of the line for which p = 2 and ∝ = 3000

1.	Find the equation of the line for which p = 2 and ∝ = 3000
Answer» Given: p = 2 and ∝ = 3000 Here p is the perpendicular that makes an angle ∝ with positive direction of x-axis, hence the equation of the straight line is given by: Formula used: X cos ∝ + y sin ∝ = p X cos 3000 + y sin 3000 = 2 i.e; cos 3000 = cos ((8×360) +120) = cos((8×2π )+120) = cos 120 = cos(180-60) = cos60 similarly, sin 3000 = sin ((8×360) +120) = sin((8×2π )+120) = sin 120 = sin(180 - 60) = - sin 60 hence, x cos 60 + y (–sin 60) = 2 x × (1/2) - y × (√3/2) = 2 Hence The required equation of the line is x - √3y = 4

Answer»

Given: p = 2 and ∝ = 3000

Here p is the perpendicular that makes an angle ∝ with positive direction of x-axis, hence the equation of the straight line is given by:

Formula used:

X cos ∝ + y sin ∝ = p

X cos 3000 + y sin 3000 = 2

i.e; cos 3000 = cos ((8×360) +120) = cos((8×2π )+120) = cos 120 = cos(180-60) = cos60

similarly, sin 3000 = sin ((8×360) +120) = sin((8×2π )+120) = sin 120

= sin(180 - 60) = - sin 60

hence, x cos 60 + y (–sin 60) = 2

x × (1/2) - y × (√3/2) = 2

Hence The required equation of the line is x - √3y = 4

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