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called the directrix, the x-axis being the axis of symmetry. So the equation of a parabola

whose vertex is
2
(0,0) and the focus is ( , 0) is = 4 .
Based on the above formula it can be concluded that = 12 is the equation of a
2
2
parabola whose vertex is (0,0). Since the general shape of the parabola is =
4 , so that we get 4 = 12 = 3. Thus the focus is ( , 0) = (3,0). On the

other hand, parabola whose peak is at (0,0) and the focus is at (– 4,0) at where =

2
4; so the equation is = 16 .

The image on the right shows a parabola that the peak
is ( , ) and the focus is ( + , ). If used new

′
′
axis with translation = = ; then the
equation of the parabola ′ = 4 ′ will be obtained.
2
If the old axis is used, it will we get the equation of a

2
parabola ( – ) = 4 ( – ) whose vertex is at the
point ( , ) and the focus is in ( + , ).

2
Based on the formula ( – ) = 4 ( – ) above, it
2
can be concluded that ( – 2) = 4.3( – 5) is the equation of a parabola whose
vertex is at (5, 2) and the focus is at (5 + 3, 2). So vice versa, a parabola whose

vertex is at (−4,3) and the focus is at (– 6, 3) where = 4, = 3, and = 2;

2
so the equation is ( – 3) = 4. (−2)( + 4) – 6 + 8 + 25 = 0 .
2

ACTIVITY 2

1. Find the equation of a parabola with a focus (5.4) and a vertex at (2,4). Then draw a

sketch of the graph and determine the directrix equation!

Answer :

The peak ( , ) (2,4).

The focus of ( + , ) ( 2 + 3,4) = (5,4).

So the parabola opens to the right. The standard form of this parabolic equation

2
is( − ) = 4 ( – )  ( − 4) = 4 (3) ( – 2)
2

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