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KCET2012MathematicsCircle

If the straight line 3 x+4 y=k touches the circle x²+y²=16 x , then the value of k is

Options

  1. A16,64
  2. B-16,-64
  3. C-16,64
  4. D16,-64

Correct answer

C. -16,64

Step-by-step solution

aligned & Given, x²+y²=16 x & x²-16 x+y²=0 & x²-2(x) 8+(8)²-(8)²+y²=0 & (x-8)²+y²=64 aligned Centre =(8,0) and radius =8 Since, the straight line 3 x+4 y=k touches the circle x²+y²=16 , therefore the length of perpendicular from the centre (8,0) to the straight line 3 x+4 y-k=0 is equal to the radius of the circle. aligned i.e., & 8 &= | 3(8)+4(0)-k 9 +16 | & 8 &= | 24-k 25 | & 8 &= |24-k| 5 & & 24-k &=40 aligned Taking positive sign, we get aligned & 24- k &=40 & &- k &=40-24=16 k &=-16 aligned Taking negative sig

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