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COMEDK2017MathematicsStraight Lines

Let P Q R be a right angled isosceles triangle, right angled at P(2,1) . If the equation of Q R is 2 x+y=3 , then the combined equation of the lines P Q and P R is

Options

  1. A3 x²-3 y²+8 x y+20 x+10 y+25=0
  2. B3 x²-3 y²+8 x y-20 x-10 y+25=0
  3. C3 x²-3 y²+8 x y+10 x+15 y+20=0
  4. D3 x²-3 y²-8 x y-10 x-15 y-20=0

Correct answer

B. 3 x²-3 y²+8 x y-20 x-10 y+25=0

Step-by-step solution

Let m be the slope of P Q . Slope of Q R is -2 aligned & | m+2 1-2 m |= 4 =1 & m+2= (1-2 m) m=3,- 1 3 aligned The lines P Q and P R are y-1 x-2 =3,- 1 3 The combined equation is (3 x-y-5)(x+3 y-5)=0 or 3 x²-3 y²+8 x y-20 x-10 y+25=0

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