Download Circle - translations and General Form

Circle ­ translations and General Form
Topic: Translation of a Circle
Do Now: Write the answers to last night's HW on the board
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Circle ­ translations and General Form
http://www.mathwarehouse.com/geometry/circle/interactive­circle­equation.php
Shifting the circle left/right changes the x value of the center
Shifting the circle up/down changes the y value of the center
Expanding/compressing the circle changes the r value
Questions:
1.) How does increasing or decreasing the h value effect the graph?
2.) How does increasing or decreasing the k value effect the graph?
3.) How does increasing or decreasing the r value effect the graph?
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Circle ­ translations and General Form
EXAMPLES:
1.) x2 + y2 = 16 is translated 3 units right and 2 units down. Find the new equation. Sketch both circles.
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Circle ­ translations and General Form
2.) x2 + y2 = 24 is translated 3 units left and 5 units down. Write the equation of the new circle.
3.) (x ­ 5)2 + (y ­ 3)2 = 9 is translated 4 units right and 2 units down. Write the equation of the new circle.
4.) (x ­ 3)2 + (y + 2)2 = 25 is translated 5 units left and 3 units up. Write the equation of the new circle.
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Circle ­ translations and General Form
General Form of the Equation of a Circle:
x2 + y2 + Dx + Ey + F = 0, where D, E, and F are constants.
EXAMPLES:
1.)
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Circle ­ translations and General Form
2.)
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