Post on 02-Jan-2016
EOC Practice
Question of the Day
Graphing and Writing
Equations of Circles
Standard Form of a Circle
Center is at (h, k)
2 2 2x y rh k
r is the radius of the
circle
2 2A 0x By Cx Dy E
General Form of a Circle
• Every binomial squared has been multiplied out.
• Every term is on the left side, equal to 0.
• Squared terms go first in alpha order.
General Form of a Circle
EX 1 Write an equation of a circle with center (3, -2) and a radius of 4.
2 2 2+x h y k r
22 23 + 2 4x y
2 23 + 2 16x y
EX 2 Write an equation of a circle with center (-4, 0) and a diameter of 10.
2 2 2+x h y k r
2 2 24 + 0 5x y
2 24 +y 25x
EX 3 Write an equation of a circle with center (2, -9) and a radius of .
11
2222 9 11x y
2 2 2+x h y k r
2 22 + 9 11x y
EX 4 Find the coordinates of the center and the measure of the radius.
2 26 + 3 25x y
The center is
The radius is
The equation is
5. Find the center, radius, & equation of the circle.
(0, 0)
12
x2 + y2 = 144
The center is
The radius is
The equation is
6. Find the center, radius, & equation of the circle.
(1, -3)
7
(x – 1)2 + (y + 3)2 = 49
7. Graph the circle, identify the center & radius.(x – 3)2 + (y – 2)2 =
9
Center (3, 2)
Radius of 3
Converting from General to Standard
1. A needs to be 1. Divide if needed.
2. Move the x terms together and the y terms together.
3. Move E to the other side of the equals sign.
4. Complete the square (as needed) for x.
5. Complete the square(as needed) for y.
6. Factor the left & simplify the right.
2 2( 8 ) 7 x x y
8. Write the standard equation of the circle. State the center & radius.
2 2 8 7 0x y x
Center: (4, 0) radius: 3
2 2( 4) 9x y
2 2( 8 )16 167 x x y
2 24 6 3 x x y y
9. Write the standard equation of the circle. State the center & radius.
2 2 4 6 3 0 x y x y
Center: (-2, 3) radius: 4
2 22 3 16 x y
2 24 6 9394 4 x x y y
2 28 2 10 x x y y
10. Write the standard equation of the circle. State the center & radius.
2 22 2 16 4 20 0 x y x y
2 24 1 7 x y
2 28 2 1 116 1610 x x y y
2 2 8 2 10 0 x y x y
: (4, 1) : 7 2.6 Center Radius
11. Write the general form of the equation of the circle.
2 24 3 36 x y
22 8 16 366 9 y yx x2 28 16 36 9 06 x x y y
2 2 8 6 11 0 x y x y
3 64 334 x y yx22 4 4 1 3 363 96 y y yx x x
HomeworkWorksheet
12 problems