Question

Let $A,B$ be two fixed points. lf $PA+PB=K$ then observe the following lists
LIST-I LIST- II
$A)K=AB$, Locus of $P$ is 1) $A$ Hyperbola
$B)K>AB$, Locus of $P$ is 2) $A$ line segment
$C)K<AB$, Locus of $P$ is 3) $A$n Ellipse
4)Empty set

• A. A -2 , B - 3 , C - 1.
• B. A - 2 , B - 3 , C - 4.
• C. A - 3 , B - 1 , C - 2.
• D. A - 2 , B - 4 , C - 1.

Answer 1

The correct option is B A - 2 , B - 3 , C - 4.

PA+PB= k
$k=AB\Rightarrow$ k is on the line
$k>AB\Rightarrow$ sum of distance of P from A and
B is constant
$\Rightarrow ellipse$
$k<AB\Rightarrow$ not possible