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AP EAMCET20224 Jul 2022Morning ShiftMathematicsCircleActual

For any two nonzero real numbers a and b if this line x a + y b = 1 is a tangent to the circle x 2 + y 2 = 1 , then which of the following is true?

Options

  1. A1 a , 1 b lies inside the circle
  2. Ba , b lies inside the circle
  3. C1 a , 1 b lies on the circle
  4. Da ,   b lies on the circle

Correct answer

C. 1 a , 1 b lies on the circle

Step-by-step solution

Given, Equation of circle as x 2 + y 2 = 1 , Now assuming a point x 1 , y 1 on circle we have equation of tangent at this point given by x x 1 + y y 1 = 1   . . . . . . . . . . . . . . . 1 , Now given x a + y b = 1 is tangent to the given circle so on comparing with equation 1 we get, x 1 = 1 a   &   y 1 = 1 b So point lie on the circle.

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