Show:
Circles
Ellipses
Hyperbolas
Parabolas
System & Classify
100

Given

(x+3)2+(y-4)2=25

Name the center and radius.

Center: (-3,4)

Radius: 5

100

What is the center of this ellipse and is it a vertical or horizontal ellipse?

(x-5)2/16  + (y+3)2/1  =1

Center: (5,-3)

Horizontal b/c 4 is larger than 1

100

What is the slope of the Asymptote? 

(y+2)2/4  -  (x-1)2/25   =1

+/- 2/5

100

Sketch a horizontal parabola where a<0

opens to the left

100

Identify this conic:

3x2+2x-9=-3y2-6y

Circle

200

Write the equation of a circle with radius 51/2 and center at (6,-9)

(x-6)2+(y+9)2=5

200

Write an equation for a vertical ellipse with center (-5,-6)

(x+5)2/small   + (y+6)2/big   = 1

200

Write the equation for the given Hyperbola. 

(see picture attached in email)

(x+4)2/9   -   (y-1)2/25   =1

200

What equation relates a and p?

a=1/(4p)

200

Identify this conic:

8x2+6x+10y2-9y-2=0

Ellipse

300

Write the equation of a circle with Diameter 16 and center (1,2)

(x-1)2+(y-2)2=64

300

Complete the square and graph this ellipse:

4x2+9y2+24x-36y+36=0

(x+3)2/9  +  (y-2)2/4  = 1

300

Graph this hyperbola

(y-2)2/4   -   (x+3)2/9   =1


(answer in email)

See graph in email

300

What is the vertex of 

x2+6x-8y-31=0

(-3,-5)

300

Identify this conic:

10(x-4)=(y+3)2

Parabola

400

What is the diameter of

(x)2+(y-8)2=7

2*root(7)

400

Write the equation of an ellipse with center (0,3), Focus (0,-2) and vertex (0,-8).

x2/96  +  (y-3)2/121  =1

c=5

a=11

so b2=96

400

Write an equation of a hyperbola with center (6,4) , vertex (1,4) and covertex (6,9).

(x-6)2/25   -   (y-4)2/25   =1

400

Complete the square and identify the type and opening direction of the parabola. What is the length of LR?

x2-12x+16y-28=0

y-4=(-1/16)(x-6)2

Vertical opens down

LR=16

400

Identify this conic:

9x2-9y2+4x-2y+6=0

Hyperbola

500

Which of the two equations is a circle and why?

6(x+1)2+6(y-7)2=30

or

4(x+3)2+6(y-4)2=24

6(x+1)2+6(y-7)2=30

Because the leading coefficients are equal, so when you divide both sides by 30 a=b which is a circle instead of an ellipse. 

500

A concert hall is designed as a semi-elliptical whispering gallery.
The hall is 100 meters long and 40 meters high.

How far from the center of the room are the foci located?

Length = 100 meters

2a=100       so    a = 50

Height = 40 meters

b=40

c2=a2-b2

c=30 meters 

500

Complete the square and graph the Hyperbola. 

25x2-16y2+50x-96y+281=0

(y+3)2/25    -  (x+1)2/16   =1

500

Find the Focus and Directrix for

x-5=(1/16)(y+2)2

Focus: (9,-2)

Directrix: x=1

500

Solve this System:

(x-3)2+(y-2)2=9

x+y=2

(0,2) and (3,-1)