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JEE Main201911 Jan 2019Morning ShiftMathematicsCircleActual

A square is inscribed in the circle x²+y²-6 x+8 y-103=0 with its sides parallel to the coordinate axes. Then the distance of the vertex of this square which is nearest to the origin is:

Options

  1. A6
  2. B137
  3. C41
  4. D13

Correct answer

C. 41

Step-by-step solution

The equation of circle is, x²+y²-6 x+8 y-103=0 (x-3)²+(y+4)²=(8 2 )²C(3,-4), r=8 2 Length of side of square = 2 r=16 P(-5,4), Q(-5,-12)R(11,-12), S(11,4) Required distance =O P= (-5-0)²+(-4-0)² = 25+16 = 41

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