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Write the parametric equation of the line passing through the point (3, 2) and making an angle 120° with the positive direction of the x-axis measured in counter clock sense and also find the coordinates of the points on the line which are at unit distance from the point (3, 2). |
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Answer» We have (x1, y1) = (3, 2), cosθ = cos 120° = −1/2 and sinθ = sin 120° = √3 /2. Therefore, the parametric equations of the line are x = x1 + γ cosθ = 3 + γ(-1/2) and y = y1 + γ sinθ = 2 + γ(√3/2) Solving these equations, we get x = 3 - γ/2 and y = 2 + γ (√3/2) Substituting γ = 1 and γ = −1 in the above coordinates, the points on the line which are at a distance of 1 unit from the point (3, 2) are obtained, respectively, (5/2, 4 + √3/2) and (7/2, 4 -√3/2) |
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