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AP EAMCET201921 Apr 2019Evening ShiftMathematicsCircleActual

Given that a > 2 b > 0 and that the line y = m x - b 1 + m 2 is a common tangent to the circles x 2 + y 2 = b 2 and ( x - a ) 2 + y 2 = b 2 . Then the positive value of m is

Options

  1. A2 b a - 2 b
  2. Bb a - 2 b
  3. Ca 2 - 4 b 2 2 b
  4. D2 b a 2 - 4 b 2

Correct answer

D. 2 b a 2 - 4 b 2

Step-by-step solution

The equation of circles are given as, x 2 + y 2 = b 2 ( x - a ) 2 + y 2 = b 2 The equation of the comment tangent for 1 st is, y = m x - b 1 + m 2 The equation of the common tangent for 2 nd circle is, y = m x - a + b 1 + m 2 Equate the common tangents, m x - b 1 + m 2 = m x - a m + b 1 + m 2 2 b 1 + m 2 = a m a 2 m 2 = 4 b 2 + 4 b 2 m 2 m 2 a 2 - 4 b 2 = 4 b 2 The value of m is, m = 2 b a 2 - 4 b 2

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