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AP EAMCET202120 Aug 2021Evening ShiftMathematicsCircleActual

The equation of the pair of straight lines parallel to x - axis and touching the circle x 2 + y 2 - 6 x - 4 y - 12 = 0 is

Options

  1. Ay 2 - 4 y - 21 = 0
  2. By 2 + 4 y - 21 = 0
  3. Cy 2 - 4 y + 21 = 0
  4. Dy 2 + 4 y + 21 = 0

Correct answer

A. y 2 - 4 y - 21 = 0

Step-by-step solution

Given that: x 2 + y 2 - 6 x - 4 y - 12 = 0 Centre of the circle: - g , - f = 3 , 2 Radius of the circle: r = g 2 + f 2 - c = 9 + 4 + 12 = 5 As we know that diameter is always perpendicular to the tangent. Hence, at the ends of the diameter perpendicular to x - axis , tangents will be parallel to x - axis . So, tangents at P 3 , 7   and Q = 3 , - 3 will be parallel to x - axis . Equation of line at P 3 , 7   and parallel to x - axis : y = 7   ⇒   y - 7 = 0 Equation of line at Q 3 , - 3 &#16

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