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AP EAMCET202120 Aug 2021Morning ShiftMathematicsCircleActual

If the circle x 2 + y 2 - 4 x - 8 y - 5 = 0 intersects the line 3 x - 4 y - m = 0 in two distinct points, then the number of integral values of ' m ' is

Options

  1. A52
  2. B51
  3. C50
  4. D49

Correct answer

D. 49

Step-by-step solution

If the circle is intersecting line 3 x - 4 y = m at two distinct points then we can say that Radius > length of perpendicular from center to the given line Perpendicular distance, P = a x 1 + b y 1 + c a 2 + b 2 ,   r = g 2 + f 2 - c ⇒ 4 + 16 + 5 > 3 2 - 4 4 - m 9 + 16 ⇒ m + 10 < 25 ⇒ m + 10 < 25   or   m + 10 > - 25 ⇒ - 35 < m < 15 There are 49 integers between - 35   &   15 So, the correct answer is 49 .

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