JEE Main20246 Apr 2024Morning ShiftMathematicsStraight LinesActual

Let a variable line of slope m>0 passing through the point (4,-9) intersect the coordinate axes at the points A and B . The minimum value of the sum of the distances of A and B from the origin is

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Correct answer

B. 25

Step-by-step solution

equation of line is aligned & y+9=m(x-4) & A= ( 9+4 m m , 0 ) & B=(0,-9-4 m) & O A+O B= 9+4 m m +9+4 m aligned aligned & m >0 & =13+ 9 ~m +4 ~m & 4 ~m + 9 ~m 2 36 4 ~m + 9 ~m 12 & OA + OB 25 aligned

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