MHT CET202313 May 2023Evening ShiftMathematicsPair of LinesActual
Let PQR be a right angled isosceles triangle, right angled at Q(2,1) . If the equation of the line PR is 2 x+y=3 , then the combined equation representing the pair of lines PQ and QR is
Options
- A3 x^2+8 x y-3 y^2-20 x-10 y+25=0
- B3 x^2-8 x y-3 y^2-20 x-10 y-25=0
- C3 x^2+8 x y-3 y^2+20 x+10 y+25=0
- D3 x^2-8 x y-3 y^2+20 x+10 y-25=0
Correct answer
A. 3 x^2+8 x y-3 y^2-20 x-10 y+25=0
Step-by-step solution
m ₁=- 1 3 or 3 Equation of PQ passing through point Q (2,1) and having slope m₁=- 1 3 is aligned & y-1=- 1 3 (x-2) & x+3 y-5=0 aligned Slope of QR = m ₂=3 [ PQ QR ] Equation of QR is aligned & y-1=3(x-2) & 3 x-y-5=0 aligned The combined equation of the lines is aligned & (x+3 y-5)(3 x-y-5)=0 & 3 x^2-3 y^2+8 x y-20 x-10 y+25=0 aligned