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AP EAMCET20226 Jul 2022Evening ShiftMathematicsCircleActual

If the line 3 x-4 y=1 touches the circle (x-1)^2+(y+2)^2=4 at ( , ) , the values of and are

Options

  1. A= 1 5 , =- 1 10
  2. B= -1 5 , =- 2 5
  3. C= -2 5 , = -11 20
  4. D= 2 5 , = 1 20

Correct answer

B. = -1 5 , =- 2 5

Step-by-step solution

( , ) lies on the line 3 x-4 y=1 array r 3 -4 =1 = (3 -1) 4 array ( , ) also lie on the circle aligned & ( -1)^2+( +2)^2=4 & ( -1)^2+ ( 3 -1 4 +2 )^2=4 & 16( -1)^2+(3 +7)^2=64 & 16 ^2+16-32 +9 ^2+49+42 =64 & 25 ^2+10 +1=0 (5 +1)^2=0 & = -1 5 & 3 ( -1 5 )-1 & and = -3-5 4 = -8 20 = -2 5 aligned

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