Circles
Given
(x+3)2+(y-4)2=25
Name the center and radius.
Center: (-3,4)
Radius: 5
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
What is the slope of the Asymptote?
(y+2)2/4 - (x-1)2/25 =1
+/- 2/5
Sketch a horizontal parabola where a<0
opens to the left
Identify this conic:
3x2+2x-9=-3y2-6y
Circle
Write the equation of a circle with radius 51/2 and center at (6,-9)
(x-6)2+(y+9)2=5
Write an equation for a vertical ellipse with center (-5,-6)
(x+5)2/small + (y+6)2/big = 1
Write the equation for the given Hyperbola.
(see picture attached in email)
(x+4)2/9 - (y-1)2/25 =1
What equation relates a and p?
a=1/(4p)
Identify this conic:
8x2+6x+10y2-9y-2=0
Ellipse
Write the equation of a circle with Diameter 16 and center (1,2)
(x-1)2+(y-2)2=64
Complete the square and graph this ellipse:
4x2+9y2+24x-36y+36=0
(x+3)2/9 + (y-2)2/4 = 1
Graph this hyperbola
(y-2)2/4 - (x+3)2/9 =1
(answer in email)
See graph in email
What is the vertex of
x2+6x-8y-31=0
(-3,-5)
Identify this conic:
10(x-4)=(y+3)2
Parabola
What is the diameter of
(x)2+(y-8)2=7
2*root(7)
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
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
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
Identify this conic:
9x2-9y2+4x-2y+6=0
Hyperbola
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.
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
Complete the square and graph the Hyperbola.
25x2-16y2+50x-96y+281=0
(y+3)2/25 - (x+1)2/16 =1
Find the Focus and Directrix for
x-5=(1/16)(y+2)2
Focus: (9,-2)
Directrix: x=1
Solve this System:
(x-3)2+(y-2)2=9
x+y=2
(0,2) and (3,-1)