The straight line x + 2y = 1 meets the coordinate axes at A and B. circle is drawn through A, B and the origin. Then the sum of perpendicular distances from A and B on the tangent to the circle at the origin is-

The straight line x + 2y = 1 meets the coordinate axes at A and B. circle is drawn through A, B and the origin. Then the sum of perpendicular distances from A and B on the tangent to the circle at the origin is-

  1. A

    5/2

  2. B

    25

  3. C

    5/4

  4. D

    45

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    Solution:

    The straight line

     · x + 2y = 1 meets the coordinate

    axes at (1, 0) and (0, 1/2).

    Since AOB=90

     Equation of circle is 

    (x1)(x0)+(y0)y12=0x2+y2xy2=0

    Now, equation of tangent at origin to the given circle

    is 2x+y=0

    Now, l1=0+124+1=125

    Similarly, l2=25 l1+l2=125+25=52

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