Question

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√2

The 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 1

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.