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AP EAMCET20228 Jul 2022Morning ShiftMathematicsCircleActual

The shortest distance from the line 3 x+4 y=25 to the circle x^2+y^2-6 x+8 y=0 is

Options

  1. A9 5
  2. B7 5
  3. C8 5
  4. D13 5

Correct answer

B. 7 5

Step-by-step solution

We have a line 3 x+4 y=25 and a circle x^2+y^2-6 x+8 y=0 for shortest distance. We draw a perpendicular from C =(3,-4) to the straight line. d = |9-16-25| 9+16 = 32 5 hence shortcut distance = 32 5 -5= 7 5

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