Question

Let $A\equiv (-3,0)$ and $B\equiv (3,0)$ be two fixed points and $P$ moves on a plane such that $PA=n\times PB(n>0)$. If $n>1$, then-

• A. $A$ lies inside the circle and $B$ lies outside the circle
• B. $A$ lies outside the circle and $B$ lies inside the circle
• C. Both $A$ and $B$ lies on the circle
• D. Both $A$ and $B$ lies inside the circle

Answer 1

Answer: (B)

$A$ lies outside the circle and $B$ lies inside the circle

for $n>1$ locus is,

$(n^2-1)(x^2+y^2)-6x(1+n^2)+9(n^2-1)=0$

putting $A(-3,0)$ we get

$9(n^2-1)+18(1+n^2)+9(n^2-1)=36n^2>0$

and putting $B(3,0)$ we get

$9(n^2-1)-18(1+n^2)+9(n^2-1)=-36<0$

$\therefore$ $A$ lies outside and $B$ lies inside the circle.