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MHT CET202523 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=0 are

Options

  1. Ax-5 y 6 26 =0
  2. Bx+5 y 6 26 =0
  3. Cx-5 y 26 =0
  4. Dx+5 y 26 =0

Correct answer

A. x-5 y 6 26 =0

Step-by-step solution

Given the circle x^2+y^2=36 with radius r=6 centered at the origin, and the line 5x+y-2=0 having slope m₁=-5 . The tangents perpendicular to this line will have slope m₂= 1 5 . Using the tangent line formula y=mx r 1+m^2 for slope 1 5 and radius 6 : y= 1 5 x 6 1+ 1 25 = 1 5 x 6 26 25 = 1 5 x 6 26 5 Multiplying through by 5 and rearranging yields x-5y 6 26 =0 , which corresponds to option A . The solution is A .

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