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EQUATION OF DIAGONAL PARABOLA

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by

Rommel Rueco

on 30 November 2014

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Transcript of EQUATION OF DIAGONAL PARABOLA

DEFINITION:
The parabola is the set of all points on a plane equidistant from a given fixed point (
focus
) and a given fixed line (
diretrix
).

The parabola is the locus of a point P which moves so that the ratio of its distance from a fixed point F (focus) and from a fixed line D (diretrix) is unity.
PARABOLA @ v(0,0) PARALLEL TO ANY OF THE COORDINATE AXIS

x = 4ay
(opens up)

x = -4ay
(opens down)

y = 4ax
(opens right)

y = -4ax
(opens left)

PARABOLA @ v(h, k) PARALLEL TO ANY OF THE COORDINATE AXIS

( x - h ) = + or - 4a(y - k)
(opens up or down)

( y - k ) = + or - 4a(x - h)
(opens right or left)

Example
parabola parallel to any of the coordinate axis
From the general equation of second degree curves which is

Ax + Cy + Dx + Ey + F = 0
, the equation of parabola is
Ax + Dx + Ey + F = 0.
(Parabola parallel to a coordinate axis)
EQUATION OF DIAGONAL PARABOLA
Parabola with axis of symmetry at y=mx+b
Rommel Rueco
Isaiah Ray Laxamana
2
2
2
2
NOTE:
either
A
or
C
is 0
2
2
2
2
2
X - 4y + 3x + 5=0
By completing the square,
(x + 3/2) = 4(y - 11/16)
2
With vertex at (-3/2, 11/16) or (-1.5, 0.7)
2
..............
EQUATION OF PARABOLA NOT PARALLEL TO ANY OF THE COORDINATE AXIS (
DIAGONAL
)
Ax + Bxy + Cy + Dx + Ey + F = 0

2
2
with
B - 4AC = 0
2
Example
1.)
x + 4xy + 4y +2x = 18y + 30

or x^2+ 4xy + 4y^2 +2x = 18y + 30
Check if it satisfies the condition:
B – 4AC = 0
B = 4
A = 1
C = 4
42 – 4(1)(4) = 0
16-16 = 0
...........
2
2
2
2.)
(x+3) + 2xy +y = 18(y + 2)
transform this equation to the equation of parabola TO CHECK. By simplifying, we have:
1x + 6x + 9 + 2xy + 1y = 18y + 36
OR


1x^2 + 6x + 9 + 2xy + 1y^2 = 18y + 36

CHECK IF IT MEETS THE CONDITION:

B – 4AC = 0
A = 1
B = 2
C = 1

4 – 4(1)(1) =

........................................
2
2
2
2
2
0
APPLICATIONS OF PARABOLA:

• Used in the design of
parabolic antennas
and
mirrors
,
searchlights
,
automobile headlights
, and
suspension bridges.

.
.
.
Full transcript