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JEE Main20244 Apr 2024Morning ShiftMathematicsCircleActual

A square is inscribed in the circle x^2+y^2-10 x-6 y+30=0 . One side of this square is parallel to y=x+3 . If (x_i, y_i ) are the vertices of the square, then (x_i^2+y_i^2 ) is equal to:

Options

  1. A148
  2. B152
  3. C160
  4. D156

Correct answer

B. 152

Step-by-step solution

y=x+c & array ll y=x+c & & x+y+d=0 | 5-3+c 2 |= 2 & | 8+d 2 |= 2 |c+2|=2 & 8+d= 2 c=0,-4 & d=-10,-6 array pts (5,5),(3,3),(7,3),(5,1) aligned & ( x _ i ^2+ y ₁^2 )=25+25+9+9+49+9+25+1 & =152 aligned

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