CK-12-Pre-Calculus Concepts

10.2. Polar Equations of Conics http://www.ck12.org

4 =c−a

2

c

5

4 =

c

a→

4

5 =

a

c→

4 c

5 =a

4 =c−

( 4 c

5

) 2

·^1 c

4 =c−^16 c

2

25 c

4 = 259 c

100

9 =c

80

9 =a

The center is the point(^1009 ,^74 π)which is much more convenient to write in polar coordinates. The closest directrix
is the liner= 4 ·sec(θ−^74 π). The other directrix is the liner=( 2 ·^1009 − 4 )·sec(θ−^74 π). One focus is at the pole,
the other focus is the point(^2009 ,^74 π). The vertices are at the center plus or minusain the same angle:(^1009 ±^809 ,^74 π)
Example C
Graph the conic from Example B.
Solution:

Concept Problem Revisited
Most calculators have a polar coordinate mode. On the TI-84, the mode can be switched to polar in the mode menu.
This changes the graphing features. You can choose to be in radians or degrees and graphs will look the same. When
you graph a circle of the formr= 8 ·cosθ. you should see the following on your calculator.