Warm up!Graph the following equation:

2 2 9x y 8

6

4

2

-2

-4

-6

-8

-10

-10 -5 5 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 9.0Completing the

Square and Circles

Conic SectionsSo I have been all fire and

brimstone…

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.2 24 4 2 1 17x x y y

Conic Equations

2 23 4 8 4 12x y y

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.

2 24 4 2 1 17x x y y Conic Equations

2 23 4 8 4 12x y y

2 2( 2) ( 1) 17x y 2 2( 1)

14 3

x y

I thought that maybe…

2 6x x

Complete the square for the given quadratic.

…just maybe…

2 8y y

Complete the square for the given quadratic.

…I’d have won the lottery by

now…

2 5a a

Complete the square for the given quadratic.

…I’d be driving a Nissan GT-R…

2 12z z

Complete the square for the given quadratic.

…the Blues would’ve won a

Cup…

24 16x x

Complete the square for the given quadratic.

…I’d be living on a beach in Mexico…

23 6x x

Complete the square for the given quadratic.

…I’d own a 5000 ft vacation

home…

27 7y y

Complete the square for the given quadratic.

…on the moon…

25 35z z

Complete the square for the given quadratic.

…and have won a Nobel

Prize…

2 2y y

Complete the square for the given quadratic.

…in awesome.

29y y

Complete the square for the given quadratic.

Circles

But no.

A circle is the set of all points equidistant from a given point

called the center.

2 2 2( ) ( )x h y k r

The equation for a circle in standard form with center (h, k)

and radius r is given by the equation:

8

6

4

2

-2

-4

-6

-8

-10

-10 -5 5 10

All those lotto tix have been

a waste…

Graph the given circle.2 28 4 16x x y y

8

6

4

2

-2

-4

-6

-8

-10

-10 -5 5 10

…I drive a Hyundai…2 2 10 0x y y

Graph the given circle.

8

6

4

2

-2

-4

-6

-8

-10

-10 -5 5 10

…the Blues haven’t been to the Finals in 40

years…2 2 2 2 47x y x y

Graph the given circle.

Find and graph the equation of the circle with the given center

and radius. 8

6

4

2

-2

-4

-6

-8

-10

-10 -5 5 10

…I still live in

the LOU…( 5, 2)

3

center

r

8

6

4

2

-2

-4

-6

-8

-10

-10 -5 5 10

…no one lives on the

moon…( 2, 9)

1

center

r

Ditto on the

directions.

8

6

4

2

-2

-4

-6

-8

-10

-10 -5 5 10

…and I keep coming in

2nd…

Graph the given circle.2 24 6 12x x y y

8

6

4

2

-2

-4

-6

-8

-10

-10 -5 5 10

…for that Nobel Prize.

Graph the given circle.2 212 14 76 0x x y y

9.0 in the packet!And your homework!