Circles Worksheet Page 2
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1
2standard form:
(x – h)
+ (y – k)
= r
2
2
2
general form of a circle: ____________________________________________________
To change from general form to standard form.
Ax
+ Cy
+ Dx + Ey + F = 0
2
2
since A & C are equal, divide through by that number (if it isn’t 1) at the very beginning!
1. move constant (F) to the other side
x
+ y
+ Dx + Ey = -F
2
2
(note: F does not have to be neg., it depends on what F was at the beginning of the problem)
2. group x terms and y terms in ( )s
(x
+ Dx) + (y
+ Ey) = -F
2
2
3. set up framework:
(x
+ Dx + ____) + (y
+ Ey + _____) = -F + _____ + _____
2
2
To find blanks, take the coefficients of x and y (D & E), divide each by 2, square the result, add in ( )s
5. Write the equation in factored form:
= G (result of -F + ___ + ___) standard form!
(x + ____)
+ (y + ____)
2
2
6. Identify the center and the radius
Write the standard form of each equation. Find the center and the radius. Sketch the graph.
5) x
+ y
+ 10x – 8y + 32 = 0
2
2
6) x
+ y
– 10x + 4y + 17 = 0
2
2
7) x
+ y
+ 12x – 4y – 60 = 0
8)
4x
– 24x + 4y
+ 16y = -51
2
2
2
2
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