Warm up!
Graph the following equation:
x  y 9
2
2
8
6
4
2
-10
-5
5
-2
-4
-6
-8
10
For your exams…
…the average was a 71%…
…the median was an 83%…
…a few people haven’t taken it yet…
…and the folks who did their HW scored
about 10% better than those who did
not!
The Wørd
Section 9.0
Completing the Square
and Circles
So I have been all fire and brimstone…
Conic Sections
A conic section is the set of all points
formed by the intersection of a plane
and a double-napped cone.
…for a few months now.
Ellipses
The planets travel in elliptical orbits.
…not circular ones.
And I think it’s because…
Hyperbolas
Comets can be slowed by the sun’s
gravity…
…I’m in a bit of
a mid-life crisis.
Conic Equations
x  4 x  4  y  2 y  1  17
2
2
3x  4 y  8 y  4  12
2
2
Conic sections are loci (the plural of
locus). A locus is the set of all points
that satisfy a given relation. A locus
may be a function, but conic sections
are not.
I’m 30.
Conic Equations
x  4 x  4  y  2 y  1  17
2
2
3x  4 y  8 y  4  12
2
2
( x  2)  ( y  1)  17
2
2
x ( y  1)

1
4
3
2
2
I thought that
maybe…
Complete the square for the given
quadratic.
x  6x 
2
…just
maybe…
Complete the square for the given
quadratic.
y  8y 
2
…I’d have won the
lottery by now…
Complete the square for the given
quadratic.
a  5a 
2
…I’d be driving a
Nissan GT-R…
Complete the square for the given
quadratic.
z  12 z 
2
…the Blues would’ve
won a Cup…
Complete the square for the given
quadratic.
4 x  16 x 
2
…I’d be living on a beach
in Mexico…
Complete the square for the given
quadratic.
3x  6 x 
2
…I’d own a 5000 ft
vacation home…
Complete the square for the given
quadratic.
7y 7y 
2
…on the moon…
Complete the square for the given
quadratic.
5 z  35 z 
2
…and have won a
Nobel Prize…
Complete the square for the given
quadratic.
y  2y 
2
…in awesome.
Complete the square for the given
quadratic.
9 y  y 
2
But no.
Circles
A circle is the set of all points
equidistant from a given point called the
center.
The equation for a circle in standard
form with center (h, k) and radius r is
given by the equation:
( x  h)  ( y  k )  r
2
2
2
Graph the given circle.
x  8x  y  4 y  16
2
2
All those lotto
tix have been a
waste…
8
6
4
2
-10
-5
5
-2
-4
-6
-8
10
Graph the given circle.
x  y  10 y  0
2
2
…I drive a
Hyundai…
8
6
4
2
-10
-5
5
-2
-4
-6
-8
10
…the Blues haven’t
been to the Finals
in 40 years…
Graph the
given circle.
x  y  2 x  2 y  47
2
2
8
6
4
2
-10
-5
5
-2
-4
-6
-8
10
Find and graph the equation
of the circle with the given
center and radius.
center  (5, 2)
r 3
…I still
live in the
LOU…
8
6
4
2
-10
-5
5
-2
-4
-6
-8
10
Ditto on the
directions.
…no one lives
on the moon…
center  (2,  9)
r 1
8
6
4
2
-10
-5
5
-2
-4
-6
-8
10
Graph the given circle.
x  4 x  y  6 y  12
2
2
…and I keep
coming in 2nd…
8
6
4
2
-10
-5
5
-2
-4
-6
-8
10
Graph the given circle.
…for that
Nobel
Prize.
x  12 x  y  14 y  76  0
2
2
8
6
4
2
-10
-5
5
-2
-4
-6
-8
10
And your homework!
9.0 in the packet!