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Maths-

General

Easy

Question

If a line AB makes an angle $theta$ with OX and is at a distance of $p$ units from the origin then the equation of AB is

x sin $θ$ ‐y cos $θ = p$
x cos $θ +$ y sin $θ = p$
x sin $θ +$ y cos $θ = p$
x cos $θ$ ‐y sin $θ = p$

The correct answer is: x sin $theta$ ‐y cos $theta equals p$

We should find the equation of the line AB
Equation of line,
$∴ y = tan θ x + c$ $c < 0$ [from diagram]
by given distance from the origin,
$c = cos θ - p$
$∴ y = x tan θ - cos θ p$
$x sin θ - y cos θ = p$

Hence choice 1 is correct

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