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AP EAMCET202124 Aug 2021Morning ShiftMathematicsStraight LinesActual

The equations of sides A B , B C and C A of a A B C are 2 x+y=0, x+p y=q and x-y=3 respectively. If P(2,3) is its orthocenter, then the value of p+q equals

Options

  1. A50
  2. B47
  3. C65
  4. D74

Correct answer

A. 50

Step-by-step solution

In A B C Equation of A B, B C and C A are 2 x+y=0 , x+P y=q and x-y=3 respectively. and P(2,3) is orthocentre. aligned & Solving aligned & 2 x+y=0 and x-y=3 & y=-2 x and x+2 x=3 & 3 x=3 & x=1, y=-2 & A(1,-2 aligned & Slope of A P= 3-(-2) 2-1 =5 & Slope of B C=- 1 p & A P B C & 5 (- 1 p )=-1 & p=5 aligned Now for vertex B aligned & 2 x+y=0, y=-2 x & x+5 y=q & x-10 x=q x=- q 9 , y= 2 q 9 & B is (- q 9 , 2 q 9 ) & Slope of B P= 2 q 9 -3 - q 9 -2 = 2 q-27 -q-18 & aligned Slope of A C=1 aligned B P A C ( q-27 -q-18 )(1)

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