If perpendicular distance of a line from origin is 4 units and angle which the normal makes with positive x-axis is 45°, then the equation will be ______________(a) x + y = 4√2(b) x – y = 4√2(c) y – x = 4√2(d) x + y = -4√2The question was posed to me in unit test.My question is based upon General Equation of a Line topic in portion Straight Lines of Mathematics – Class 11

If perpendicular distance of a line from origin is 4 units and angle w

1.	If perpendicular distance of a line from origin is 4 units and angle which the normal makes with positive x-axis is 45°, then the equation will be ______________(a) x + y = 4√2(b) x – y = 4√2(c) y – x = 4√2(d) x + y = -4√2The question was posed to me in unit test.My question is based upon General Equation of a Line topic in portion Straight Lines of Mathematics – Class 11
Answer» Right choice is (a) x + y = 4√2 Best EXPLANATION: If p is perpendicular DISTANCE of line from ORIGIN and ω be the angle FORMED by normal with positive x-axis then equation of line is x cos⁡ω + y sin⁡ω = p. So, equation of given line will be x cos⁡45° + y sin⁡45° = 4 =>(x + y)/√2 = 4 =>x + y = 4√2.

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