Analytic Geometry
Circles
Substitution
Elimination
100
Find the midpoint between A(3, 4) and B(-5, 12)
(-1, 8)
100
What is the radius of this circle?
5
100
Using substitution, what is the point of intersection (POI) for:
x + y = 14
x – y = 2
POI (8, 6)
100
Solve the following equations using the elimination method:
p + q – 40 = 0
7p + 3q = 180
p = 15 and q = 25
200
Find the distance between A(1, 4) and B (7, 12)
d = 10
200
What is the radius of the circle
x2 + y2 =100?
10
200
Solve for the variables p and q using substitution.
3p – q = 3
9p – 3q = 9
Infinite solutions
200
Find the values of a and b from the system of equations
2a + b = -4
5a – 3b = 1
a= -1
b= -2
300
Does the point (3,3) lie inside, on, or outside the circle x2 + y2 = 18 ?
On
300
What is the equation of the circle that is centered at the origin and passes through the point (4, 3)?
x2 + y2 = 25
300
Find the numbers if one number is three times of the other number. Also, given that the difference between two numbers is 26
The two numbers are 13 and 39.
300
Find two numbers if the addition of two numbers is 14, and their difference is 2
x = 8 and y = 6
400
Write the equation of the circle that is centered at (-3, 2) and goes through (-6, 4)
(x + 3)2 + (y - 2)2 = 13
400
Write the equation of a circle whose center is at (3,-2) and has a radius of 11.
(x - 3)2 + (y + 2)2 = 121
400
A rental car company is running two specials. Customers can pay $38 to rent a compact car for the first day plus $7 for each additional day, or they can rent the same car for $30 the first day and $8 for every additional day beyond that. Bella notices that, given the number of additional days she wants to rent the car for, the two specials are equivalent. How many additional days does Bella want? How much would Bella pay in total?
For 8 additional days, Bella would pay $94 either way.
Start with...
y = 7x + 38
y = 8x + 30
400
Shivani and Hassan went to an arcade where the machines took tokens. Shivani played 9 games of skee ball and 5 games of pinball, using a total of 24 tokens. At the same time, Hassan played 2 games of skee ball and 5 games of pinball, using up 17 tokens. How many tokens does each game require?
Every game of skee ball requires 1 token, and every game of pinball requires 3 tokens.
Start with...
9x + 5y = 24
2x + 5y = 17
500
Triangle ABC has coordinates A(-2, 3), B(-8, -7) and C(2, -1).
What is the equation of the median through A?
y = 7x + 17
500
The midpoint of AB is 5 cm from the center of the circle. The radius of the circle is 13 cm. What is the length of AB?
24 cm
500
Two classmates got together over the weekend to do their assigned History reading. Pam can read 1 page per minute, while Jayla can read 4 pages per minute. When they met, Pam had already read 89 pages, and Jayla had already gotten through 23 pages. After a while, they had both read the same number of pages. How long did that take? How many pages had each one read?
After 22 minutes, Pam and Jayla had each read 111 pages.
Start with...
y = x + 89
y = 4x + 23
500
Two coworkers picked up some writing instruments at the office supply store. Darell selected 7 boxes of pencils and 4 boxes of ballpoint pens, paying $22. Next, Winston spent $36 on 9 boxes of pencils and 9 boxes of ballpoint pens. How much does a box of each cost?
A box of pencils costs $2, and a box of pens costs $2.
Start with...
7x + 4y = 22
9x + 9y = 36