Search any question & find its solution
Question:
Answered & Verified by Expert
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
Options:
Solution:
2961 Upvotes
Verified Answer
The correct answer is:
$3 x^2-y^2=12$
Given $(4,0)$ and $B(-4,0)$, Let $P(x, y)$
Now, $P A-P B=4$
$\begin{aligned}
& \Rightarrow \sqrt{(x-4)^2+y^2}-\sqrt{(x+4)^2+y^2}=4 \\
& \Rightarrow 3 x^2-y^2=12
\end{aligned}$
Now, $P A-P B=4$
$\begin{aligned}
& \Rightarrow \sqrt{(x-4)^2+y^2}-\sqrt{(x+4)^2+y^2}=4 \\
& \Rightarrow 3 x^2-y^2=12
\end{aligned}$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.