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- Chapter 1: Locus
Chapter 1: Locus
#1: The locus of the point 'P' such that PA=K(PB)
(i) Perpendicular bisector of AB if K=1
(ii) A circle if K≠1
(i) Perpendicular bisector of AB if K=1
(ii) A circle if K≠1
(by Omer)         
#2: If PA+PB = K
(i) an ellipse if K>A
(ii) a line segment if K=AB
(iii) empty set if K<AB
(i) an ellipse if K>A
(ii) a line segment if K=AB
(iii) empty set if K<AB
(by Omer)         
#3: If |PA-PB|=K
(i) a hyperbola if K<AB
(ii) union of two rays if K=AB
(iii) empty set if K>AB
(i) a hyperbola if K<AB
(ii) union of two rays if K=AB
(iii) empty set if K>AB
(by Omer)         
#4: If (PA)2 + (PB)2 = K(PC)2
(i) a straight line if k=2
(ii) a circle if k≠2 and k>0
(i) a straight line if k=2
(ii) a circle if k≠2 and k>0
(by Omer)         
#5: The locus P such that angle APB=90° is a circle on the line joining A,B as the ends of the diameter.
(by Omer)         
#6: The ends of a rod of length K moves on the positive coordinate axes the locus of the point on the rod which divides it in the ratio l : m is:
x2/m2 + y2/m2 = k2/(1+m2)
x2/m2 + y2/m2 = k2/(1+m2)
(by Omer)         
#7: The curve represented by S = ax2 + by2 + 2hxy + 2gx + 2fy + c = 0 is:
- a pair of parallel lines is h2 = ab , Δ=0
- a parabola if h2 =ab , Δ≠0
- an ellipse if h <ab , Δ≠0
- a circle if a=b , h=0 ,g2 + f2 -ac ≥ 0
- a pair of intersecting lines if h2 > ab ,Δ=0
- a hyperbola if h2>ab , Δ≠0
- a rectangular hyperbola if h2>ab , a+b=0 , Δ≠0
(by Omer)