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AP EAMCET202022 Sep 2020Evening ShiftMathematicsPair of LinesActual

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

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 circle is x^2+y^2-6 x-4 y-12=0 aligned Centre & =(3,2) Radius & = (3)^2+(2)^2+12 = 9+4+12 = 25 r & =5 aligned Since, tangents are paralle to X -axis Let y=k be the tangent to the given circle y-k=0 touches the circle Perpendicular distance from C(3,2) to y-k=0= radius |2-k| 1 =5 aligned |2-k| & =5 2-k & = 5 2-k=5 (or) 2-k & =-5 k=-3 (or) k & =7 aligned Required equation of tangents are y=-3 and y=7 (y+3)=0 and (y-7)=0 Equation of pair of tangents is (y+3)(y-7)=0 y^2-4 y-21=0 Hence, option (1) is correct.

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