### Present Remotely

Send the link below via email or IM

• Invited audience members will follow you as you navigate and present
• People invited to a presentation do not need a Prezi account
• This link expires 10 minutes after you close the presentation

Do you really want to delete this prezi?

Neither you, nor the coeditors you shared it with will be able to recover it again.

# EQUATION OF DIAGONAL PARABOLA

No description
by

## Rommel Rueco

on 30 November 2014

Report abuse

#### 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
,