Study Guide Conic Section Unit
NAME: __________________________________ PERIOD: _________
DATE: ________________
1) What is the equation of the circle with center (5, -1) and radius = ¾
2) What is the equation of the circle with center (-6, 7) and radius = 5
3) Which conic section is given by the equation (x – h)n = j(y – k)m +7 when
n=1 and m = 2, and j = -6
4) Which conic section is given by the equation (x – h)n = j(y – k)m +7 when
n=2 and m = 2, and j = 14
5) What are the equations of these circles?
a.
b.
6) What is the standard form of this equation of a circle?
x2 + y2 + 12x - 4y + 25 = 0
7) What is the standard form of this equation of a circle?
Study Guide Conic Section Unit
x2 + y2 + 12x - 6y - 36 = 0
8) This equation represents which conic section?
y 2 15  x 2

21
15
9) This equation represents which conic section?
x2  y2

25
25
10) A circle with equation x2 + y2 = 7 has center (0, 0). The circle is shifted 3
units to the left and 6 units up. What is the equation of the new circle?
11) A circle with equation x2 + y2 = 2 has center (0, 0). The circle is shifted 1
unit to the right and 3 units up. What is the equation of the new circle?
12) What is the standard form of the equation for a circle with center (7, -1)
and area of 81
13) What is the standard form of the equation for a circle with center (-8, -4)
and area of 16
14) This equation 10x2 + 8y2 = 80 represents what conic section?
MCHS 2013-2014 Algebra 2
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Study Guide Conic Section Unit
15) This equation 8x2 - 9y2 = 72 represents what conic section?
16) Find the center and radius of the circle with equation
x2 + y2 - 6x + 4y + 9 = 0
17) Find the center and radius of the circle with equation
x2 + y2 + 2x - 4y - 4 = 0
18) What conic section does this equation represent, and what is its center?
( x  9) 2 ( y  2) 2

1
25
16
19) What conic section does this equation represent, and what is its center?
( x  1) 2 ( y  2) 2

1
49
25
20) What conic section does this equation represent, and what is its center?
( y  1) 
( x  2) 2
1
25
21) A circle is tangent to the y-axis at (0, 5) and the line y = -1. What is the
equation of this circle?
22) A circle is tangent at the origin and the line x = 4. What is the equation of
this circle?
23) Consider the circle with the equation (x – 5)2 + (y + 1)2 = 9.
MCHS 2013-2014 Algebra 2
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Study Guide Conic Section Unit
a. What are the center and radius of the circle? Explain how you
determined your answer.
b. Joey says (5, -1) is a point on the circle. Is Joey correct? Show your
work algebraically, and explain how you made your decision.
c. Graph the circle. Explain the procedure you used to graph the circle.
MCHS 2013-2014 Algebra 2
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