Circles Hyperbolas Simultaneous Equations (Intersections) Factorization
100
radius: 7
center: (0,0)
What is the radius and center of the following circle:
x² + y² = 49
100
Table of values to be shown on the board.

x = 0
y = 0
Create a table of values for the following hyperbola:
y = 2/x
What are the asymptotes?
100
(-2, -1), (1, 2)
Find the coordinates of the points of intersection of the line x+1 with the circle x² + y² = 5.
100
(x+6)(x+2)
Factorize:
x² + 8x + 12
200
radius: 1
center: (2, -7)
What is the radius and center of the following circle:
(x-2)²+(y+7)² = 1
200
x = 3
y = 0
What are the horizontal and vertical asymptotes for
y = 1/(x-3)
200
(0,4), (4,0)
Find the coordinates of the points of intersection of x²+y² = 16 and y = -x+4
200
(x-3)(x-4)
Factorize:
x² - 7x + 12
300
x² + (y-1)² = 16
Write down the equation for a circle with center of (0,1) and a radius of 4.
300
Done on board.
Sketch both hyperbolas:
y = -1/x and y = 1/x
Label the hyperbola with the correct equation.
300
(0,5), (-4, -3)
Find the coordinates of the point of intersection of
y = 2x+5 and x² + y² = 25
300
(x-7)(x+3) = 0
x = 7, -3
Factorize & Solve:
x² - 4x - 21 = 0
400
(x+5)²+(y-3)² = 81
Write down the equation for a circle with center of (-5,3) and a radius of 9.
400
Sketch done on board (DESMOS).
Asymptotes:
y = 2
x = 0
Use a table of values to sketch the hyperbola
y = 1/x + 2
State both vertical and horizontal asymptotes.
400
(1, 2), (-2, -1)
Find the coordinates of intersection for y = 2/x and
y = x+1
400
(x-3)(x-2) = 0
x = 3, 2
Factorize & Solve:
3x² - 15x + 18 = 0
500
Center: (1,2)
Radius: 2
x-int: (1,0)
y-int: (0, 3.73) and (0, 0.27) --> using the quadratic formula
To earn full points for this, you must identify the center and radius of circle, sketch the graph, and find the x and y intercepts.
(x-1)²+(y-2)² = 4
500
Hyperbola on DESMOS.

y = 0
x = 0
Use a table of values to sketch the hyperbola
y = -4/x
State both vertical and horizontal asymptotes.
500
(1, -1), (-1, 1)
Find the coordinates of intersection for y = -1/x and
y = -x
500
x(x+7)=0
x = 0, -7
Factorize and Solve:
x² + 7x = 0






Pre-Methods Math Circles, Hyperbolas, and Simultaneous Equations Review

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