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AP EAMCET202119 Aug 2021Morning ShiftMathematicsCircleActual

Let L 1 be a straight line passing through the origin and L 2 be the straight line x + y = 1 . If the intercepts made by the circle x 2 + y 2 - x + 3 y = 0 on L 1 and L 2 are equal, then which of the following equations represent L 1

Options

  1. Ax + y = 0   &   x + 7 y = 0
  2. Bx − y = 0   &   x + 7 y = 0
  3. Cx − 7 y = 0   &   x + y = 0
  4. Dx − 7 y = 0   &   x − y = 0

Correct answer

B. x − y = 0   &   x + 7 y = 0

Step-by-step solution

Given line L 2   ≡ x + y - 1 = 0 Let a straight line passing through origin and having slope m will be L 1   ≡   y - m x   =   0 Given circle x 2 + y 2 - x + 3 y = 0 Here centre =   C =   - g , - f   =   1 2 , - 3 2   &   r   =   g 2 + f 2   = 10 2 . Given that intercepts made by the lines are equal i.e both the lines will be equidistant from centre. We know that perpendicular distance from x 1 ,   y 1 to a x + b y + c = 0 &#

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