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MHT CET202522 Apr 2025Evening ShiftMathematicsCircleActual

The equations of the tangents to the circle x^2+y^2=36 which are perpendicular to the line 5 x+y=2 , are

Options

  1. Ax+5 y 6 26 =0
  2. Bx-5 y 6 26 =0
  3. C5 x-y 6 26 =0
  4. D5 x+y 6 26 =0

Correct answer

B. x-5 y 6 26 =0

Step-by-step solution

The circle x^2 + y^2 = 36 has radius r = 6 . The line 5x + y = 2 rewritten as y = -5x + 2 has slope m₁ = -5 . Since the tangents are perpendicular to this line, their slopes satisfy m₁ m₂ = -1 . Solving (-5)m₂ = -1 gives m₂ = 1 5 . The tangent lines to the circle with slope m are given by y = mx r 1 + m^2 . Substituting m = 1 5 and r = 6 : y = 1 5 x 6 1 + ( 1 5 )^2 = 1 5 x 6 26 25 = 1 5 x 6 26 5 Multiplying through by 5: 5y = x 6 26 Rewriting in standard form: x - 5y 6 26 = 0 This corresponds to option B .

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