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AP EAMCET20225 Jul 2022Evening ShiftMathematicsStraight LinesActual

Suppose P(x,y)lying on 3 x-y+2=0 or 3 x+y-2=0 is at a distance of 5 units from their point of intersection. Then the distance from (0,0) to the foot of the perpendicular of P onto the y -axis is

Options

  1. A2
  2. B5 3 2
  3. C2+ 5 3 2
  4. D2- 5 3 2

Correct answer

A. 2

Step-by-step solution

L ₁: 3 x-y+2=0 aligned & L ₂: 3 x+y-2=0 & ~L ₁ and L ₂ intersect on A(0,2) & P can be on any of L ₁ or L ₂ & such that AP =5 aligned For L ₁: y= 3 x+2 i.e. m= 3 aligned & ABO =60^ & BAO =30^ & PAQ =30^ aligned aligned & In PAQ, & 30^ =A Q / A P aligned aligned & AQ = AP 30^ = 5 3 2 & OQ = OA + AQ aligned =2+ 5 3 2

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