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AP EAMCET202315 May 2023Morning ShiftMathematicsProperties of TrianglesActual

Let S be the circumcircle of the triangle formed by the line x-2 y-4=0 with the coordinate axes. If P (-2,-4) is a point in the plane of the circle S and Q is a point on S such that the distance between P and Q is the least, then PQ =

Options

  1. A5 5
  2. B5+ 5
  3. C13+ 5
  4. D13- 5

Correct answer

A. 5 5

Step-by-step solution

Line x-2 y-4=0 intersect the axes at A(4,0) and B(0,-2) aligned & Centre of circle = ( 4+0 2 , -2+0 2 )=(2,-1) & radius = (2-0)^2+(0+1)^2 = 5 & C P= (2+2)^2+(-1+4)^2 =5 aligned Distance of P Q is least when points P, Q and C are collinear. P Q=C P-C Q=5- 5

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