Transcript No Slide Title

PF1  PF2  2a
Definition
b
a
c
Center
at(h,k)
An ellipse with major axis
parallel to x-axis
Important Idea
2
2
2
a>b
a b c
b
a
c
(h,k)
Definition
The standard form of the
equation of an ellipse when
the major axis is parallel to
the x-axis
( x  h) ( y  k )


1
2
2
a
b
2
2
Definition
An ellipse
with
major
axis
parallel
to y-axis
a b c
2
2
2
a
c
b
Center:
at (h,k)
Definition
The standard form of the
equation of an ellipse when
the major axis is parallel to
the y-axis
( x  h) ( y  k )


1
2
2
b
a
2
2
Important Idea
The
of the majoris
If thedirection
larger denominator
axis is determined by the
under
the
x
term,
the
larger denominator. The
ellipse
is “fat”; if theislarger
larger denominator
2
always
a in the
standard
denominator
is under
the y
equation.
term, the ellipse is “skinny”
Try This
For the following ellipse, find
the coordinates of the center,
foci, vertices, & endpoints of
the minor axis. Then graph.
x ( y  4)

1
36
25
2
2
Solution x  ( y  4)  1
2
36
2
25
Center:(0,-4)
Foci: ( 11, 4)
Vertices: (±6,-4)
Minor Axes Ends(0,1),(0,-9)
Try This
Write an equation of the
ellipse with Foci (3,2) and
(3,-4) and whose major axes
is 14 units long.
Solution
( x  3) ( y  1)

1
40
49
2
2
How is the “roundness” of an
ellipse measured?
Try This
For the following ellipse, find
the coordinates of the center,
foci, vertices, & endpoints of
the minor axis. Then graph.
x  25 y  6 x 100 y  84  0
2
2
( x  3) ( y  2)

1
Solution
25
1
2
2
Center:(3,2)
Foci: (3  24, 2)
Vertices: (-2,2) (8,2)
Minor Axes Ends(3,3),(3,1)
Another
For the following ellipse, find
the coordinates of the center,
foci, vertices, & endpoints of
the minor axis. Then graph.
9x  16 y  36x  96 y  36  0
2
2
( x  2) ( y  3)

1
Solution
16
9
2
2
Center:(2,-3)
Foci: (2  7, 3)
Vertices: (6,-3) (-2,-3)
Minor Axes Ends(2,-6),(2,0)