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A straight line is drawn through the point P(2;3) and is inclined at an angle of `30^@` with the x-axis . Find the coordinates of two points on it at a distance 4 from point P.

Text Solution

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Here, `P (x_(1), y_(1)) -= P(2,3), theta = 30^(@).`
So, the required coordinates of points at distance 4 units from point P are
`(x_(1) +- r "cos" theta, y_(1)+- r "sin" theta)`
` -= (2+- 4 "cos" 30^(@), 3+- 4 "sin" 30^(@))`
`-= (2+- 4 (sqrt(3))/(2), 3+-4(1)/(2))`
`-= (2+2sqrt(3), 5), (2-2sqrt(3),1)`
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