Q81 / 160 · AP EAMCET 2023 (15 May Shift 2) · Mathematics
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
- Correct answerA$3 x^2-y^2=12$
- B$x^2-3 y^2=12$
- C$4\left(x^2-3 y^2\right)=1$
- D$3 x^2-y^2=1$
Solution
Given $(4,0)$ and $B(-4,0)$, Let $P(x, y)$
Now, $P A-P B=4$
$\begin{aligned}
& \Rightarrow \sqrt{(x-4)^2+y^2}-\sqrt{(x+4)^2+y^2}=4 \\
& \Rightarrow 3 x^2-y^2=12
\end{aligned}$
Hence, the correct answer is option: 'A'.