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AP EAMCET20224 Jul 2022Morning ShiftMathematicsCircleActual

The length of the intercept on the line 4 x - 3 y - 10 = 0 by the circle x 2 + y 2 - 2 x + 4 y - 20 = 0 is

Options

  1. A5
  2. B2
  3. C10
  4. D6

Correct answer

C. 10

Step-by-step solution

Given, Circle x 2 + y 2 - 2 x + 4 y - 20 = 0 Now center will be   1 ,   - 2 So, the line 4 x - 3 y - 10 = 0 passes through center Then length of the intercept equal to diameter of circle So, radius r = g 2 + f 2 - c = 1 + 4 + 20 = 5 So, diameter d = 2 r = 2 × 5 = 10

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