AP EAMCET · Maths · Circle
If \(A(4,0)\) and \(B(-4,0)\) are two points, then the locus of a point \(\mathrm{P}\) such that \(\mathrm{PA}-\mathrm{PB}=4\) is
- A \(3 x^2-y^2=12\)
- B \(x^2-3 y^2=12\)
- C \(4\left(x^2-3 y^2\right)=1\)
- D \(3 x^2-y^2=1\)
Answer & Solution
Correct Answer
(A) \(3 x^2-y^2=12\)
Step-by-step Solution
Detailed explanation
Given \((4,0)\) and \(B(-4,0)\), Let \(P(x, y)\) Now, \(P A-P B=4\) \(\begin{aligned} & \Rightarrow \sqrt{(x-4)^2+y^2}-\sqrt{(x+4)^2+y^2}=4 \\ & \Rightarrow 3 x^2-y^2=12 \end{aligned}\)
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