TS EAMCET · Maths · Circle
If the angle between a pair of tangents drawn from a point \(P\) to the circle \(x^2+y^2-4 x+2 y+3=0\) is \(\frac{\pi}{2}\) then, the locus of \(P\) is
- A \(x^2+y^2-2 x+2 y+3=0\)
- B \(x^2+y^2-8 x+4 y+2=0\)
- C \(x^2+y^2+4 x+2 y+1=0\)
- D \(x^2+y^2-4 x+2 y+1=0\)
Answer & Solution
Correct Answer
(D) \(x^2+y^2-4 x+2 y+1=0\)
Step-by-step Solution
Detailed explanation
Given, equation of circle \(x^2+y^2-4 x+2 y+3=0\), Now required locus of point \(P\) is \((x-2)^2+(y+1)^2=2(4+1-3)\) \(\begin{aligned} & \Rightarrow \quad x^2+y^2-4 x+2 y+5=4 \\ & \Rightarrow \quad x^2+y^2-4 x+2 y+1=0\end{aligned}\) Hence, option (d) is correct.
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