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ea of the13. A line formas a triangle in the first quadrant with coordinates axes. If the area oftriangle is 54y3 sq, units and the perpendicular drawn from the origin to the linemakes an angle 60° with x-axis, find the equation of the line. |
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Answer» A line AB forms a triangle with coordinate axes of area 54√3 square unit and also perpendicular drawn from the origin to the line makes an angle of 60° with x -axis as shown in figure. area of triangle = 1/2 × height × base see attachment, height = a and base = b then, area of triangle = 1/2ab = 54√3 ⇒ab = 108√3 ------(1) Now, Let P is the length of perpendicular drawn from origin to line Then, cos60° = P/b ⇒b = P/cos60° = 2P cos30° = P/a ⇒a = P/cos30° = 2P/√3 Now, put a and b value in equation (1), 4P²/√3 = 108√3 ⇒P² = 108 × 3 P = ±18 , but we have to take only P = 18 because triangle is in 1st quadrant .a = 2P/√3 = 36/√3 = 12√3b = 2P = 36 so, equation of line : cos60°x + sin60° y= P x + √3y - 36 = 0 Hence, equation of line : x + √3y -36 = 0 |
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