TS EAMCET · Maths · Straight Lines
If \(A=(1,2), B=(2,1)\) and \(P\) is any point satisfying the condition \(P A+P B=3\), then the equation of the locus of \(P\) is
- A \(16 x^2+7 y^2-64 x-48=0\)
- B \(x^2+10 x y+25 y^2-34 x-170 y=0\)
- C \(32 x^2+8 x y+32 y^2-108 x-108 y+99=0\)
- D \(4 x^2+12 x y+9 y^2-20 x-30 y=0\)
Answer & Solution
Correct Answer
(C) \(32 x^2+8 x y+32 y^2-108 x-108 y+99=0\)
Step-by-step Solution
Detailed explanation
(c) Let the point \(P(x, y)\) such that for two points \(A(1,2)\) and \(B(2,1)\), \(P A+P B=3\) \(\Rightarrow \sqrt{(x-1)^2+(y-2)^2}+\sqrt{(x-2)^2+(y-1)^2}=3\) \(\Rightarrow \sqrt{(x-1)^2+(y-2)^2}=3-\sqrt{(x-2)^2+(y-1)^2}\) On squaring both sides, we get…
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