9.1
Circles
and
Parabolas
Objective:
To
write
equations
of
circles
and
parabolas
in
standard
form.
I.
Circles
General
Form
:
____________________________________________________________________
Standard
Form:
____________________________________________
Examples:
Write
the
standard
form
of
the
equation
of
the
circle
with
the
given
center
and
radius.
Then
sketch
a
graph
of
the
circle.
1. Center
(0,0),
radius
=8
2. Center
(‐3,5),
r=3
Example:
Give
the
center
and
radius
of
the
circle
described
by
the
equation,
and
graph
each
equation.
3.
x 2 + y 2 = 49 2
2
4.
( x + 1) + ( y − 4 ) = 25 €
€
5.
3x 2 + 3y 2 = 27 6.
x 2 + y 2 + 8x + 4 y + 16 = 0 €
€
II:
Parabolas
A
parabola
is
the
set
of
all
points
in
a
plane
that
are
equidistant
from
a
fixed
line
called
the
___________________
and
a
fixed
point
called
the
___________________,
not
on
the
line.
The
midpoint
between
the
focus
and
the
directrix
is
called
the
_____________________
and
the
line
passing
through
the
focus
and
the
vertex
is
the
___________________
of
the
parabola.
Standard
Form:
__________________________________________________________________
Vertical
axis,
directrix:
______________________;
focus
____________________
__________________________________________________________________
Horizontal
axis,
directrix:
____________________;
focus
___________________
P
is
the
directed
distance
from
__________________________________________________________
or
from
_______________________________________________________________
Example
1:
Find
the
standard
form
of
the
equation
of
the
parabola
with
the
given
information.
a.
Vertex:
(5,2)
Focus:
(3,2)
b.
Vertex:
(‐2,1)
Directrix:
x=1
Example
2:
Find
the
vertex,
focus,
and
directrix
of
the
parabola
and
sketch
its
graph.
a.
y 2 = 3x €
b.
x 2 + 4 x + 6y − 2 = 0 €