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

Step-by-step solution

array ll & Slope of Q R=-2 . & Slope of P Q= m ₁ & 45^ = | m ₁+2 1+ m ₁(-2) | & 1= | m ₁+2 1-2 ~m ₁ | & m ₁=- 1 3 array Equation of PQ passing through point P (2,1) and having slope -1 3 is aligned & y-1=- 1 3 (x-2) & 3(y-1)+(x-2)=0 aligned Slope of PR = m ₂=3 equation of PR is aligned & y-1=3(x-2) & (y-1)-3(x-2)=0 aligned The joint equation of the lines is aligned & [3(y-1)+(x-2)][(y-1)-3(x-2)]=0 & 3(y-1)^2-8(y-1)(x-2)-3(x-2)^2=0 & 3 (x^2-4 x+4 )+8(x y-x-2 y+2) & -3 (y^2-2 y+1 )=0 & 3 x^2-3 y^2+8 x y-20 x-10 y+25=