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TS EAMCET · Maths · Circle

From a point \(A(1,0)\) on the circle \(x^2+y^2-2 x+2 y+1=0\), a chord \(A B\) is drawn and it is extended to a point \(P\) such that \(A P=3 A B\). The equation of the locus of \(P\) is

  1. A \(x^2+y^2-2 x+6 y+1=0\)
  2. B \(x^2+y^2-2 x+4 y+1=0\)
  3. C \(x^2+y^2-2 x+8 y-8=0\)
  4. D \(x^2+y^2-2 x+3 y+1=0\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(x^2+y^2-2 x+6 y+1=0\)

Step-by-step Solution

Detailed explanation

Let the point \(P(h, k), A(1,0)\) and \(B\left(x_2, y_1\right)\). We have, \(A P=3 A B\) \( \begin{aligned} \Rightarrow & A B+B P & =3 A B \\ \Rightarrow & B P & =2 A B \Rightarrow \frac{A B}{B P}=\frac{1}{2} \end{aligned} \) \(\therefore B\) divided \(A P\) in the ratio…