Let A ≡ (a, 0) and B ≡ (– a, 0) be two fixed points ∀ a ∈(–∞,0) and P moves on a plane such that PA = nPB(n ≠ 0).
On the basis of above information, answer the following questions:
1. If |n| ≠ 1 , then the locus of a point P is
a. a straight line
b. a circle
c. a parabola
d. an ellipse
2. If n = 1, then the locus of a point P is
a. a straight line
c. a circle
c. a parabola
d. a hyperbola
3. If 0 < 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
4. If n > 1, then
a. A lies outside the circle and B lies inside 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
5. If focus of P is a circle, then the circle
a. passes through A and B
b. never passes through A and B
c. passes through A but does not pass through B
d. passes through B but does not pass through A
