If $A(4,0)$ and $B(-4,0)$ are two points, then the locus of a point $\mathrm{P}$ such that…

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
  1. $3 x^2-y^2=12$
  2. $x^2-3 y^2=12$
  3. $4\left(x^2-3 y^2\right)=1$
  4. $3 x^2-y^2=1$

Solution

Given $(4,0)$ and $B(-4,0)$, Let $P(x, y)$ Now, $P A-P B=4$ $\begin{aligned} & \Rightarrow \sqrt{(x-4)^2+y^2}-\sqrt{(x+4)^2+y^2}=4 \\ & \Rightarrow 3 x^2-y^2=12 \end{aligned}$

Asked in: AP EAMCET 2023 (15 May Shift 2)

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