ExamBro
ExamBro
TS EAMCET · Maths · Straight Lines

If \(A(2,3)\) and \(B(3,-2)\) are two fixed points and \(P(x, y)\) is a variable point satisfying the condition \(|P A-P B|=2\), then the locus of \(P\) is

  1. A \((x+y+1)^2=4\left[(x-3)^2+(y+2)^2\right]\)
  2. B \((x-5 y-2)^2=4\left[(x-2)^2+(y-3)^2\right]\)
  3. C \((x-5 y-2)^2=4\left[(x-3)^2+(y+2)^2\right]\)
  4. D \((x+y+1)^2=4\left[(x-2)^2+(y-3)^2\right]\)
Verified Solution

Answer & Solution

Correct Answer

(C) \((x-5 y-2)^2=4\left[(x-3)^2+(y+2)^2\right]\)

Step-by-step Solution

Detailed explanation

According to question, \(\begin{gathered} |P A-P B|=2 \\ \Rightarrow \sqrt{(x-2)^2+(y-3)^2}-\sqrt{(x-3)^2+(y+2)^2}=2 \\ \Rightarrow \sqrt{(x-2)^2+(y-3)^2}=2+\sqrt{(x-3)^2+(y+2)^2} \end{gathered}\) On squaring, we get…