4. Locus of a Parabola
• The locus of a point is a parabola
whose vertex is at the origin and
whose directrix is parallel to one of the
axes if and only if its equation in
standard form is:
• 1. x2 = 4cy if its focus is (0,c)
• 2. x2 = -4cy if its focus is (0,-c)
• 3. y2 = 4cx if its focus is (c,0)
• 4. y2 = -4cx if its focus is(-c,0)
• With c>0
6. Locus of a Transformed
Parabola
• 1. (x-h)2 = 4c (y-k) if its focus is (0,c)
• 2. (x-h)2 = -4c(y-k) if its focus is (0,-c)
• 3. (y-k)2 = 4c (x-h) if its focus is (c,0)
• 4. (y-k)2 = -4c(x-h) if its focus is(-c,0)
• With c>0
7. Inequalities of a Parabola
• The interior of a Parabola is:
• 1. x2 < 4cy if its focus is (0,c)
• 2. x2 < -4cy if its focus is (0,-c)
• 3. y2 < 4cx if its focus is (c,0)
• 4. y2 < -4cx if its focus is(-c,0)
• For the exterior, change < to >
8. Exam Question
•
To give a concert, the orchestra conductor and the musicians must take their places on a
rectangular stage. The conductor stands in the centre of the front of the stage.
Rear wall
Conductor
The musicians must be positioned in such a way that they are equidistant from the conductor and
the rear wall of the stage.
Which geometric locus will be formed by the group of musicians?
A) A straight line C) A hyperbola
B) An ellipse D) A parabola
9. Exam Question
•
As illustrated in the adjacent diagram, a circle whose
centre coincides with the vertex of a parabola, also cuts it
at a point with coordinates (7, y). The equation of the
parabola is :
x2
6x + 4y + 17 = 0.
What is the equation of the circle?
x
y
(7, y)
A) (x 3)2
+ (y + 2)2
= 32 C) (x 3)2
+ (y 2)2
= 32
B) (x 3)2
+ (y + 2)2
= 49 D) (x 3)2
+ (y 2)2
= 49
