Example 11 - Line perpendicular distance from origin is 4 units - Examples

  1. Chapter 10 Class 11 Straight Lines
  2. Serial order wise
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Example 11 Find the equation of the line whose perpendicular distance from the origin is 4 units and the angle which the normal makes with positive direction of x-axis is 15°. We need to find equation of line Perpendicular distance of AB from origin is 4 units & angle which the normal makes with (+)ve direction of x-axis is 15° By Normal from Equation of line is x cos ω + y sin ω = p where, p = normal distance from the origin & ω = angle which makes by the normal with positive x-axis Here p = 4 & ω = 15° Putting values x cos ω + y sin ω = p x cos 15° + y sin 15° = 4 x ((√3 + 1)/(2√2)) + y ((√3 − 1)/(2√2)) = 4 (𝑥(√3 + 1) + 𝑦(√3 − 1))/(2√2) = 4 x(√3 + 1) + y(√3 − 1) = 4 × 2√2 (√3 + 1)x + (√3 − 1)y = 8√2 Which Is the required equation

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