A straight line is drawn through the point p(2, 3) and is inclined at an angle of 30Âş with the x-axis. Then coordinates of two points on it at a distance 4 from p are
Answers
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x - √3y= 2 - 3√3 , (2 + 2√3 , 5) & (2 - 2√3 , 5) are at a distance of 4 from p
Step-by-step explanation:
Straight line Inclined at an angle of 30° with the x-axis.
Slope of line = Tan30 = 1/√3
y = x/√3 + C
Passes through p(2 , 3)
=> 3 = 2/√3 + C
=> C = (3√3 - 2)/√3
y = x/√3 + (3√3 - 2)/√3
=>√3y = x + 3√3 - 2
=> x - √3y= 2 - 3√3
=> x - 2 = √3(y -3)
coordinates of two points on it at a distance 4 from p are
(x - 2)² + (y - 3)² = 4²
=> (√3(y -3))² + (y - 3)² = 4²
=> (y - 3)² (3 + 1) = 4²
=> (y - 3)² = 4
=> y - 3 = ±2
=> y = 5 , - 1
y = 5
x -2 = √3(y -3) = 2√3 => x = 2 + 2√3
(2 + 2√3 , 5)
y = 1
x -2 = √3(y -3) = -2√3 => x = 2 - 2√3
(2 - 2√3 , 5)
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