TS EAMCET · Maths · Straight Lines
Let \(\mathrm{A}=(1,2), \mathrm{B}=(2,1), \mathrm{C}=(-1,-1)\) be three points. If \(\mathrm{P}\) is a point such that the area of the quadrilateral \(\mathrm{PABC}\) is twice the area of the triangle \(\mathrm{PAB}\), then the equation of the locus of \(\mathrm{P}\) is
- A \(8 x^2-14 x y+3 y^2-18 x+22 y+7=0\)
- B \(9 x^2-12 x y+4 y^2-24 x+16 y+16=0\)
- C \(x^2+2 x y+y^2-6 x-6 y+9=0\)
- D \(x^2-4 x y+8 y-4=0\)
Answer & Solution
Correct Answer
(D) \(x^2-4 x y+8 y-4=0\)
Step-by-step Solution
Detailed explanation
Let \(P(x, y)\) \[ \operatorname{Ar}(P A B C)=\frac{1}{2}\left|\begin{array}{cc} x & y \\ 1 & 2 \\ 2 & 1 \\ -1 & -1 \\ x & y \end{array}\right| \]…
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